JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}\) and \(\vec{b}\) be two vectors such that \(|\vec{b}|=1\) and \(|\vec{b} \times \vec{a}|=2\). Then \(|(\vec{b} \times \vec{a})-\vec{b}|^2\) is equal to
- A \(3\)
- B \(5\)
- C \(1\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(5\)
Step-by-step Solution
Detailed explanation
\(|\vec{b}|=1 \&|\vec{b} \times \vec{a}|=2 \) \((\vec{b} \times \vec{a}) \cdot \vec{b}=\vec{b} \cdot(\vec{b} \times \vec{a})=0 \) \(|(\vec{b} \times \vec{a})-\vec{b}|^2=|\vec{b} \times \vec{a}|^2+|\vec{b}|^2 \) \(=4+1=5\)
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
- Let a circle of radius 4 pass through the origin O, the points A \( (-\sqrt{3}a,0) \) and \( B(0,-\sqrt{2}b) \), where a and b are real parameters and \( ab\ne0 \). Then the locus of the centroid of \( \Delta OAB \) is a circle of radiusJEE Mains 2026 Easy
- Let \(\mathrm{a}_{1}, \mathrm{a}_{2}, \mathrm{a}_{3}, \ldots\) be an \(A.P.\) If \(\frac{a_{1}+a_{2}+\ldots+a_{10}}{a_{1}+a_{2}+\ldots+a_{p}}=\frac{100}{p^{2}}, p \neq 10\), then \(\frac{a_{11}}{a_{10}}\) is equal to :JEE Mains 2021 Hard
- The probabilities that players \(A\) and \(B\) of a team are selected for the captaincy for a tournament are \(0.6\) and \(0.4\), respectively. If \(A\) is selected the captain, the probability that the team wins the tournament is \(0.8\) and if \(B\) is selected the captain, the probability that the team wins the tournament is \(0.7\). Then the probability, that the team wins the tournament, is :JEE Mains 2026 Easy
- The value of \(\int\limits_{0}^{2\pi } {\left[ {\sin \,2x\left( {1 + \cos \,3x} \right)} \right]} \,dx\) where \([t]\) denotes the greatest integer function, isJEE Mains 2019 Hard
- Let \(A=\left[a_{i j}\right]\) be \(3 \times 3\) matrix such that \(A\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right], A\left[\begin{array}{l}4 \\ 1 \\ 3\end{array}\right]=\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]\) and \(A\left[\begin{array}{l}2 \\ 1 \\ 2\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]\), then \(a_{23}\) equals :JEE Mains 2025 Easy
- Let \(\mathrm{P}\) be a plane passing through the points \((2,1,0),(4,1,1)\) and \((5,0,1)\) and \(R\) be any point \((2,1,6) .\) Then the image of \(\mathrm{R}\) in the plane \(\mathrm{P}\) isJEE Mains 2020 Hard
More PYQs from JEE Mains
- If \(\mathrm{U}_{\mathrm{n}}=\left(1+\frac{1}{\mathrm{n}^{2}}\right)\left(1+\frac{2^{2}}{\mathrm{n}^{2}}\right)^{2} \ldots\left(1+\frac{\mathrm{n}^{2}}{\mathrm{n}^{2}}\right)^{\mathrm{n}}\), then \(\lim _{n \rightarrow \infty}\left(U_{n}\right)^{\frac{-4}{n^{2}}}\) is equal to :JEE Mains 2021 Hard
- The number of real roots of the equation \(e^{6 x}-e^{4 x}-2 e^{3 x}-12 e^{2 x}+e^{x}+1=0\) is:JEE Mains 2021 Hard
- \(5 -\) digit numbers are to be formed using \(2, 3, 5, 7, 9\) without repeating the digits. If \(p\) be the number of such numbers that exceed \(20000\) and \(q\) be the number of those that lie between \(30000\) and \(90000\), then \(p : q\) isJEE Mains 2013 Hard
- Let \(f : R \to R\) be differentiable at \(c \in R\) and \(f(c) = 0\). If \(g\left( x \right) = \left| {f\left( x \right)} \right|\) , then at \(x =c, g\) isJEE Mains 2019 Hard
- A fair die is tossed repeatedly until a six is obtained. Let \(\mathrm{X}\) denote the number of tosses required and let \(\mathrm{a}=\mathrm{P}(\mathrm{X}=3), \mathrm{b}=\mathrm{P}(\mathrm{X} \geq 3)\) and \(\mathrm{c}=\) \(\mathrm{P}(\mathrm{X} \geq 6 \mid \mathrm{X}>3)\). Then \(\frac{\mathrm{b}+\mathrm{c}}{\mathrm{a}}\) is equal toJEE Mains 2024 Hard
- \(\smallint \left( {1 + x - \frac{1}{x}} \right){e^{x + \frac{1}{x}}}\;dx = \)JEE Mains 2014 Hard