STD 11 - Vectors PYQs: JEE Mains Physics

Showing 1–41 of 41 questions

1. 1. Two particles are located at equal distance from origin. The position vectors of those are represented by \(\bar{A}=2 \hat{i}+3 n \hat{j}+2 \hat{k}\) and \(\bar{B}=2 \hat{i}-2 \hat{j}+4 p \hat{k}\), respectively. If both the vectors are at right angle to each other, the value of \(\mathrm{n}^{-1}\) is _____ . 2025 Medium
2. 2. A vector has magnitude same as that of \(\overrightarrow{\mathrm{A}}-=3 \hat{\mathrm{j}}+4 \hat{\mathrm{j}}\) and is parallel to \(\overrightarrow{\mathrm{B}}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}\). The \(\mathrm{x}\) and \(y\) components of this vector in first quadrant are \(\mathrm{x}\) and \(3\) respectively where  \(x\)= _______. 2024 Hard
3. 3. For three vectors \(\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k})\), \(\vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k})\) and \(\vec{C}=(-8 \hat{i}-\hat{j}+3 \hat{k})\), if \(\overrightarrow{\mathrm{A}} \cdot(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{C}})=0\), them value of \(\mathrm{x}\) is _______. 2024 Hard
4. 4. If \(\vec{a}\) and \(\vec{b}\) makes an angle \(\cos ^{-1}\left(\frac{5}{9}\right)\) with each other, then \(|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|\) for \(|\vec{a}|=n|\vec{b}|\) The integer value of \(n\) is _______. 2024 Hard
5. 5. If two vectors \(\vec{A}\) and \(\vec{B}\) having equal magnitude \(\mathrm{R}\) are inclined at an angle \(\theta\), then... 2024 Hard
6. 6. The angle between vector \(\vec{Q}\) and the resultant of \((2 \overrightarrow{\mathrm{Q}}+2 \overrightarrow{\mathrm{P}})\) and \((2 \overrightarrow{\mathrm{Q}}-2 \overrightarrow{\mathrm{P}})\) is _______. 2024 Hard
7. 7. The resultant of two vectors \(\vec{A}\) and \(\vec{B}\) is perpendicular to \(\overrightarrow{\mathrm{A}}\) and its magnitude is half that of \(\vec{B}\). The angle between vectors \(\vec{A}\) and \(\vec{B}\) is _______. 2024 Hard
8. 8. Three vectors \(\overrightarrow{\mathrm{OP}}, \overrightarrow{\mathrm{OQ}}\) and \(\overrightarrow{\mathrm{OR}}\) each of magnitude \(A\) are acting as shown in figure. The resultant of the three vectors is \(A \sqrt{x}\). The value of \(x\) is _______.
   2024 Hard
9. 9. Two forces \(\vec{F}_1\) and \(\vec{F}_2\) are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between \(\vec{F}_1\) and \(\overrightarrow{\mathrm{F}}_2\) is \(\cos ^{-1}\left(\frac{1}{\mathrm{n}}\right)\). The value of \(|\mathrm{n}|\) is __________. 2024 Hard
10. 10. A vector in \(x-y\) plane makes an angle of \(30^{\circ}\) with \(y\)-axis The magnitude of \(y\)-component of vector is \(2 \sqrt{3}\). The magnitude of \(x\)-component of the vector will be 2023 Medium
11. 11. If \(\overrightarrow{ P }=3 \hat{ i }+\sqrt{3} \hat{ j }+2 \hat{ k }\) and \(\overrightarrow{ Q }=4 \hat{ i }+\sqrt{3} \hat{ j }+2.5 \hat{ k }\) then, The unit vector in the direction of \(\overrightarrow{ P } \times \overrightarrow{ Q }\) is \(\frac{1}{x}(\sqrt{3} \hat{i}+\hat{j}-2 \sqrt{3} \hat{k})\). The value of \(x\) is 2023 Medium
12. 12. If two vectors \(\vec{P}=\hat{i}+2 m \hat{j}+m \hat{k}\) and \(\vec{Q}=4 \hat{i}-2 \hat{j}+ mk\) are perpendicular to each other. Then, the value of \(m\) will be : 2023 Medium
13. 13. Two forces having magnitude \(A\) and \(\frac{ A }{2}\) are perpendicular to each other. The magnitude of their resultant is 2023 Easy
14. 14. Vectors \(a \hat{i}+b \hat{j}+\hat{k}\) and \(2 \hat{i}-3 \hat{j}+4 \hat{k}\) are perpendicular to each other when \(3 a+2 b=7\), the ratio of a to \(b\) is \(\frac{x}{2}\). The value of \(x\) is \(..............\) 2023 Hard
15. 15. When vector \(\overrightarrow{ A }=2 \hat{ i }+3 \hat{ j }+2 \hat{ k }\) is subtracted from vector \(\vec{B}\), it gives a vector equal to \(2 \hat{j}\). Then the magnitude of vector \(\vec{B}\) will be: 2023 Easy
16. 16. \(\vec{A}\) is a vector quantity such that \(|\vec{A}|=\) nonzero constant. Which of the following expressions is true for \(\vec{A}\) \(?\) 2022 Easy
17. 17. A person moved from \(A\) to \(B\) on a circular path as shown in figure. If the distance travelled by him is \(60 \,m\), then the magnitude of displacement would be\(.....\,m\) (Given \(\left.\cos 135^{\circ}=-0.7\right)\)
    2022 Hard
18. 18. If \(\overrightarrow{ A }=(2 \hat{ i }+3 \hat{ j }-\hat{ k }) \;m\) and \(\overrightarrow{ B }=(\hat{ i }+2 \hat{ j }+2 \hat{ k })\; m\). The magnitude of component of vector \(\overrightarrow{ A }\) along vector \(\vec{B}\) will be \(......m\). 2022 Medium
19. 19. If the projection of \(2 \hat{i}+4 \hat{j}-2 \hat{k}\) on \(\hat{i}+2 \hat{j}+\alpha \hat{k}\) is zero. Then, the value of \(\alpha\) will be. 2022 Hard
20. 20. Two vectors \(\overrightarrow{ A }\) and \(\overrightarrow{ B }\) have equal magnitudes. If magnitude of \(\overrightarrow{ A }+\overrightarrow{ B }\) is equal to two times the magnitude of \(\overrightarrow{ A }-\overrightarrow{ B }\), then the angle between \(\overrightarrow{ A }\) and \(\overrightarrow{ B }\) will be ....................... 2022 Medium
21. 21. Which of the following relations is true for two unit vectors \(\hat{ A }\) and \(\hat{ B }\) making an angle \(\theta\) to each other\(?\) 2022 Hard
22. 22. Assertion \(A\) : If \(A, B, C, D\) are four points on a semi-circular arc with centre at \('O'\) such that \(|\overrightarrow{{AB}}|=|\overrightarrow{{BC}}|=|\overrightarrow{{CD}}|\), then \(\overrightarrow{{AB}}+\overrightarrow{{AC}}+\overrightarrow{{AD}}=4 \overrightarrow{{AO}}+\overrightarrow{{OB}}+\overrightarrow{{OC}}\) Reason \(R\) : Polygon law of vector addition yields \(\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C D}+\overrightarrow{A D}=2 \overrightarrow{A O}\) In the light of the above statements, choose the most appropriate answer from the options given below
    2021 Hard
23. 23. If \(\vec{A}\) and \(\vec{B}\) are two vectors satisfying the relation \(\vec{A} . \vec{B}=[\vec{A} \times \vec{B}]\). Then the value of \([\vec{A}-\vec{B}]\). will be : 2021 Medium
24. 24. If \(\overrightarrow{ P } \times \overrightarrow{ Q }=\overrightarrow{ Q } \times \overrightarrow{ P },\) the angle between \(\overrightarrow{ P }\) and \(\overrightarrow{ Q }\) is \(\theta\left(0^{\circ} < \theta < 360^{\circ}\right) .\) The value of \(\theta\) will be ........ 2021 Medium
25. 25. In an octagon \(ABCDEFGH\) of equal side, what is the sum of \(\overrightarrow{ AB }+\overrightarrow{ AC }+\overrightarrow{ AD }+\overrightarrow{ AE }+\overrightarrow{ AF }+\overrightarrow{ AG }+\overrightarrow{ AH }\) if, \(\overrightarrow{ AO }=2 \hat{ i }+3 \hat{ j }-4 \hat{ k }\)
    2021 Hard
26. 26. Statement \(I:\) If three forces \(\vec{F}_{1}, \vec{F}_{2}\) and \(\vec{F}_{3}\) are represented by three sides of a triangle and \(\overrightarrow{{F}}_{1}+\overrightarrow{{F}}_{2}=-\overrightarrow{{F}}_{3}\), then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement \(II:\) A triangle made up of three forces \(\overrightarrow{{F}}_{1}, \overrightarrow{{F}}_{2}\) and \(\overrightarrow{{F}}_{3}\) as its sides taken in the same order, satisfy the condition for translatory equilibrium. In the light of the above statements, choose the most appropriate answer from the options given below: 2021 Medium
27. 27. Statement \(I :\)Two forces \((\overrightarrow{{P}}+\overrightarrow{{Q}})\) and \((\overrightarrow{{P}}-\overrightarrow{{Q}})\) where \(\overrightarrow{{P}} \perp \overrightarrow{{Q}}\), when act at an angle \(\theta_{1}\) to each other, the magnitude of their resultant is \(\sqrt{3\left({P}^{2}+{Q}^{2}\right)}\), when they act at an angle \(\theta_{2}\), the magnitude of their resultant becomes \(\sqrt{2\left({P}^{2}+{Q}^{2}\right)}\). This is possible only when \(\theta_{1}<\theta_{2}\). Statement \(II :\) In the situation given above. \(\theta_{1}=60^{\circ} \text { and } \theta_{2}=90^{\circ}\) In the light of the above statements, choose the most appropriate answer from the options given below 2021 Hard
28. 28. The angle between vector \((\overrightarrow{{A}})\) and \((\overrightarrow{{A}}-\overrightarrow{{B}})\) is :
    2021 Hard
29. 29. The magnitude of vectors \(\overrightarrow{ OA }, \overrightarrow{ OB }\) and \(\overrightarrow{ OC }\) in the given figure are equal. The direction of \(\overrightarrow{ OA }+\overrightarrow{ OB }-\overrightarrow{ OC }\) with \(x\)-axis will be
    2021 Hard
30. 30. The resultant of these forces \(\overrightarrow{O P}, \overrightarrow{O Q}, \overrightarrow{O R}, \overrightarrow{O S}\) and \(\overrightarrow{{OT}}\) is approximately \(\ldots \ldots {N}\). [Take \(\sqrt{3}=1.7, \sqrt{2}=1.4\) Given \(\hat{{i}}\) and \(\hat{{j}}\) unit vectors along \({x}, {y}\) axis \(]\)
    2021 Medium
31. 31. Three particles \({P}, {Q}\) and \({R}\) are moving along the vectors \({A}=\hat{{i}}+\hat{{j}}, {B}=\hat{{j}}+\hat{{k}}\) and \({C}=-\hat{{i}}+\hat{{j}}\) respectively. They strike on a point and start to move in different directions. Now particle \(P\) is moving normal to the plane which contains vector \(\vec{A}\) and \(\vec{B} .\) Similarly particle \(Q\) is moving normal to the plane which contains vector \(\vec{A}\) and \(\vec{C} .\) The angle between the direction of motion of \(P\) and \(Q\) is \(\cos ^{-1}\left(\frac{1}{\sqrt{x}}\right)\). Then the value of \(x\) is ...... . 2021 Hard
32. 32. Two vectors \(\vec A\) and \(\vec B\) have equal magnitudes. The magnitude of \((\vec A + \vec B)\) is \(‘n’\) times the magnitude of \((\vec A - \vec B)\). The angle between \( \vec A\) and \(\vec B\) is 2021 Hard
33. 33. Two vectors \(\overrightarrow{{X}}\) and \(\overrightarrow{{Y}}\) have equal magnitude. The magnitude of \((\overrightarrow{{X}}-\overrightarrow{{Y}})\) is \({n}\) times the magnitude of \((\overrightarrow{{X}}+\overrightarrow{{Y}})\). The angle between \(\overrightarrow{{X}}\) and \(\overrightarrow{{Y}}\) is - 2021 Hard
34. 34. What will be the projection of vector \(A=\hat{i}+\hat{j}+\hat{k}\) on vector \(\vec{B}=\hat{i}+\hat{j}\). 2021 Medium
35. 35. The sum of two forces \(\overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) is \(\overrightarrow{\mathrm{R}}\) such that \(|\overrightarrow{\mathrm{R}}|=|\overrightarrow{\mathrm{P}}| .\) The angle \(\theta\) (in degrees) that the resultant of \(2 \overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) will make with \(\overrightarrow{\mathrm{Q}}\) is 2020 Medium
36. 36. A particle is moving along a circular path with a constant speed of \(10\,ms^{-1}.\) What is the magnitude of the change in velocity of the particle, when it moves through an angle of \(60^{o}\) around the centre of the circle .......... \(m/s\) 2019 Medium
37. 37. In the cube of side \(a\) shown in the figure, the vector from the central point of the face \(ABOD\) to the central point of the face \(BEFO\) will be
    2019 Medium
38. 38. Let \(\left| {{{\vec A}_1}} \right| = 3,\,\left| {\vec A_2} \right| = 5\), and \(\left| {{{\vec A}_1} + {{\vec A}_2}} \right| = 5\). The value of \(\left( {2{{\vec A}_1} + 3{{\vec A}_2}} \right)\cdot \left( {3{{\vec A}_1} - 2{{\vec A}_2}} \right)\) is 2019 Hard
39. 39. Two forces \(P\) and \(Q\), of magnitude \(2F\) and \(3F\), respectively, are at an angle \(\theta \) with each other. If the force \(Q\) is doubled, then their resultant also gets doubled. Then, the angle \(\theta \) is ....... \(^o\) 2019 Medium
40. 40. Let \(\vec A\, = \,(\hat i\, + \,\hat j)\,\)  and \(\vec B\, = \,(2\hat i\, - \,\hat j)\,.\)  The magnitude of a coplanar vector \(\vec C\) such that  \(\vec A\cdot \vec C\, = \,\vec B\cdot \vec C\, = \vec A\cdot \vec B\) is given by 2018 Hard
41. 41. A vector \(\vec A \) is rotated by a small angle \(\Delta \theta\) radian \(( \Delta \theta << 1)\) to get a new vector \(\vec B\) In that case \(\left| {\vec B - \vec A} \right|\) is 2015 Medium

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