JEE Mains · Maths · STD 12 - 10. vector algebra
If \(\left| {\vec a} \right| = 2,\left| {\vec b} \right| = 3\) and \(\left| {2\,\vec a - \vec b} \right| = 5\), then \(\left| {2\,\vec a + \vec b} \right|\) equals
- A \(17\)
- B \(7\)
- C \(5\)
- D \(1\)
Answer & Solution
Correct Answer
(C) \(5\)
Step-by-step Solution
Detailed explanation
Given \(|2 \vec{a}-\vec{b}|=5\) \(\sqrt{(2|\vec{a}|)^{2}+|\vec{b}|^{2}-2 \times|2 \vec{a}| \vec{b} | \cos \theta}=5\) Putting values of \(|\vec a|\) and \(|\vec{b}|,\) we get \( \Rightarrow (2 \times 2)^{2}+(3)^{2}-24 \cos \theta=25 \) \( \Rightarrow \cos \theta=0\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If the four complex numbers \(z\), \(\overline{ z }, \overline{ z }-2 \operatorname{Re}(\overline{ z })\) and \(z -2 \operatorname{Re}( z )\) represent the vertices of a square of side \(4\) units in the Argand plane, then \(|z|\) is equal toJEE Mains 2020 Hard
- Consider the following two binary relations on the set \(A= \{a, b, c\}\) : \(R_1 = \{(c, a) (b, b) , (a, c), (c,c), (b, c), (a, a)\}\) and \(R_2 = \{(a, b), (b, a), (c, c), (c,a), (a, a), (b, b), (a, c)\}.\) ThenJEE Mains 2018 Hard
- If \(\frac{{dy}}{{dx}} + y\tan x = \sin 2x\) and \(y(0)\,=1\) , then \(y(\pi)\) is equal toJEE Mains 2014 Hard
- The sum of coefficients of integral power of \(x\) in the binomial expansion \({\left( {1 - 2\sqrt x } \right)^{50}}\) is :JEE Mains 2015 Hard
- The integral \(\int_0^\pi \frac{8 x d x}{4 \cos ^2 x+\sin ^2 x}\) is equal toJEE Mains 2025 Medium
- Let \(z\) be a complex number such that \(\left|\frac{z-2 i}{z+i}\right|=2, z \neq-i\). Then \(z\) lies on the circle of radius \(2\) and centreJEE Mains 2023 Hard
More PYQs from JEE Mains
- The inverse function of \(f(\mathrm{x})=\frac{8^{2 \mathrm{x}}-8^{-2 \mathrm{x}}}{8^{2 \mathrm{x}}+8^{-2 \mathrm{x}}}, \mathrm{x} \in(-1,1),\) isJEE Mains 2020 Hard
- The number of integral values of \(m\) for which the equation \((1 + m^2) x^2 - 2(1 + 3m) x + (1 + 8m) = 0\) has no real root isJEE Mains 2019 Hard
- Twenty metres of wire is available for fencing off a flowerbed in the form of a circular sector. Then the maximum area (in sq. m) of the flower bed is :JEE Mains 2017 Hard
- Let \(\alpha, \beta\) be the roots of the quadratic equation \(x^2+\sqrt{6} x+3=0\). Then \(\frac{\alpha^{23}+\beta^{23}+\alpha^{14}+\beta^{14}}{\alpha^{15}+\beta^{15}+\alpha^{10}+\beta^{10}}\) is equal toJEE Mains 2023 Hard
- Let \(\overrightarrow{ x }\) be a vector in the plane containing vectors \(\overrightarrow{ a }=2 \hat{ i }-\hat{ j }+\hat{ k }\) and \(\overrightarrow{ b }=\hat{ i }+2 \hat{ j }-\hat{ k }\). If the vector \(\overrightarrow{ x }\) is perpendicular to \((3 \hat{ i }+2 \hat{ j }-\hat{ k })\) and its projection on \(\overrightarrow{ a }\) is \(\frac{17 \sqrt{6}}{2},\) then the value of \(|\overrightarrow{ x }|^{2}\) is equal to ...... .JEE Mains 2021 Medium
- Let \(f:[-1,2] \rightarrow \mathrm{R}\) be given by \(f(x)=2 x^2+x+\left[x^2\right]-[x]\), where \([t]\) denotes the greatest integer less than or equal to \(t\). The number of points, where \(f\) is not continuous, is :JEE Mains 2024 Hard