JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}=\hat{i}+\hat{j}+2 \hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}\) and \(\overrightarrow{ c }=\hat{ i }-\hat{ j }+\hat{ k }\) be three given vectors. Let \(\vec{v}\) be a vector in the plane of \(\vec{a}\) and \(\overrightarrow{ b }\) whose projection on \(\overrightarrow{ c }\) is \(\frac{2}{\sqrt{3}}\). If \(\overrightarrow{ v } . \hat{ j }=7\), then \(\overrightarrow{ v } \cdot(\hat{ i }+\hat{ k })\) is equal to
- A \(6\)
- B \(7\)
- C \(8\)
- D \(9\)
Answer & Solution
Correct Answer
(D) \(9\)
Step-by-step Solution
Detailed explanation
\(\overrightarrow{ v }=\lambda \overrightarrow{ a }+\mu \overrightarrow{ b }\) \(\vec{v}=\lambda(1,1,2)+\mu(2,-3,1)\) \(\vec{v}=(\lambda+2 \mu, \lambda-3 \mu, 2 \lambda+\mu)\) \(\overrightarrow{ v } \cdot \hat{ j }=7\) \(\lambda-3 \mu=7\)…
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
- Tangents drawn from the point \((- 8, 0)\) to the parabola \(y^2\, = 8x\) touch the parabola at \(P\) and \(Q\). If \(F\) is the focus of the parabola, then the area of the triangle \(PFQ\) (in sq. units) is equal toJEE Mains 2018 Hard
- The integral \(\int_{\frac{\pi }{{12}}}^{\frac{\pi }{4}} {\frac{{8\,\cos \,2x}}{{{{\left( {\tan \,x + \cot \,x} \right)}^3}}}\,dx} \) equalsJEE Mains 2017 Hard
- For the system of linear equations : \(x-2 y=1, x-y+k z=-2, k y+4 z=6, k \in R\) consider the following statements : \((A)\) The system has unique solution if \(k \neq 2\), \(k \neq-2\) \((B)\) The system has unique solution if \(k =-2\). \((C)\) The system has unique solution if \(k =2\). \((D)\) The system has no-solution if \(k =2\). \((E)\) The system has infinite number of solutions if \(k \neq-2\) Which of the following statements are correct?JEE Mains 2021 Medium
- Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be 2a and 2b, respectively, and one focus and the corresponding directrix of this hyperbola be \((-5,0)\) and \(5 x+9=0\), respectively. If the product of the focal distances of a point \((\alpha, 2 \sqrt{5})\) on the hyperbola is \(p\), then \(4 p\) is equal toJEE Mains 2025 Medium
- The number of four -digit numbers strictly greater than \(4321\) that can be formed using the digits \(0, 1, 2, 3, 4, 5\) (repetition of digits is allowed) isJEE Mains 2019 Hard
- Among the relations \(S =\left\{( a , b ): a , b \in R -\{0\}, 2+\frac{ a }{ b } > 0\right\}\) And \(T =\left\{( a , b ): a , b \in R , a ^2- b ^2 \in Z \right\}\),JEE Mains 2023 Hard
More PYQs from JEE Mains
- The value of \(\int_{-\pi}^\pi \frac{2 y(1+\sin y)}{1+\cos ^2 y} d y\) is :JEE Mains 2024 Hard
- Let \(A\) and \(B\) be two independent events such that \(\mathrm{P}(\mathrm{A})=\frac{1}{3}\) and \(\mathrm{P}(\mathrm{B})=\frac{1}{6} .\) Then, which of the following is TRUE?JEE Mains 2020 Hard
- Let \(f(x)=2+|x|-|x-1|+|x+1|, x \in R\). Consider \((S1)\): \(f^{\prime}\left(-\frac{3}{2}\right)+f^{\prime}\left(-\frac{1}{2}\right)+f^{\prime}\left(\frac{1}{2}\right)+f^{\prime}\left(\frac{3}{2}\right)=2\) \(( S 2): \int_{-2}^{2} f ( x ) dx =12\)Then,JEE Mains 2022 Hard
- Let \(\theta\) be the angle between the planes \(P_1=\vec{r} \cdot(\hat{ i }+\hat{ j }+2 \hat{ k })=9\) and \(P _2=\overrightarrow{ r } \cdot(2 \hat{ i }-\hat{ j }+\hat{ k })=15\).Let \(L\) be the line that meets \(P _2\) at the point \((4,-2,5)\) and makes an angle \(\theta\) with the normal of \(P_{2^*}\) If \(\alpha\) is the angle between \(L\) and \(P_2\) then \(\left(\tan ^2 \theta\right)\left(\cot ^2 \alpha\right)\) is equal to \(...........\).JEE Mains 2023 Easy
- The number of \(3-\)digit numbers, that are divisible by either \(2\) or \(3\) but not divisible by \(7\) is \(.........\).JEE Mains 2023 Hard
- Let \(A =\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]\) and \(B =\left[\begin{array}{l}\alpha \\ \beta\end{array}\right] \neq\left[\begin{array}{l}0 \\ 0\end{array}\right]\) such that
\(AB = B\) and \(a + d =2021,\) then the value of \(ad - bc\) is equal to ...... .JEE Mains 2021 Medium