JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{b}=\hat{i}+\hat{j}+\lambda \hat{k}, \lambda \in R\). If \(\vec{a}\) is a vector such that \(\overrightarrow{ a } \times \overrightarrow{ b }=13 \hat{ i }-\hat{ j }-4 \hat{ k } \quad\) and \(\quad \overrightarrow{ a } \cdot \overrightarrow{ b }+21=0\), then \((\vec{b}-\vec{a}) \cdot(\hat{k}-\hat{j})+(\vec{b}+\vec{a}) \cdot(\hat{i}-\hat{k})\) is equal to
- A \(36\)
- B \(22\)
- C \(14\)
- D \(19\)
Answer & Solution
Correct Answer
(C) \(14\)
Step-by-step Solution
Detailed explanation
\((\overrightarrow{ a } \times \overrightarrow{ b }) \cdot \overrightarrow{ b }=0\) \(\Rightarrow 13-1-4 \lambda=0 \Rightarrow \lambda=3\)…
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
- \(\lim _{n \rightarrow \infty} \frac{3}{n}\left\{4+\left(2+\frac{1}{n}\right)^2+\left(2+\frac{2}{n}\right)^2+\ldots+\left(3-\frac{1}{n}\right)^2\right\}\) is equal toJEE Mains 2023 Hard
- Consider the following system of equations : \(x+2 y-3 z=a\) ; \(2 x+6 y-11 z=b\) ; \(x-2 y+7 z=c\) where \(a , b\) and \(c\) are real constants. Then the system of equations :JEE Mains 2021 Medium
- If the domain of the function
\(f(x)=\frac{1}{\sqrt{10+3 x-x^2}}+\frac{1}{\sqrt{x+|x|}}\) is \((a, b)\), then \((1+a)^2+b^2\) is equal to :JEE Mains 2025 Easy - The value of \(\cot \left(\sum\limits_{n=1}^{50} \tan ^{-1}\left(\frac{1}{1+n+n^{2}}\right)\right)\) isJEE Mains 2022 Hard
- Let \(A=\left[a_{i j}\right]\) be a matrix of order \(3 \times 3\), with \(a_{i j}=(\sqrt{2})^{i+j}\). If the sum of all the elements in the third row of \(A^2\) is \(\alpha+\beta \sqrt{2}, \alpha, \beta \in \mathbf{Z}\), then \(\alpha+\beta\) is equal to :JEE Mains 2025 Easy
- Let \(A=\left[\begin{array}{ccc}\cos \theta & 0 & -\sin \theta \\ 0 & 1 & 0 \\ \sin \theta & 0 & \cos \theta\end{array}\right]\). If for some \(\theta \in(0, \pi)\), \(A^2=A^T\), then the sum of the diagonal elements of the matrix \((\mathrm{A}+\mathrm{I})^3+(\mathrm{A}-\mathrm{I})^3-6 \mathrm{~A}\) is equal to _____ .JEE Mains 2025 Easy
More PYQs from JEE Mains
- A differential equation representing the family of parabolas with axis parallel to \(\mathrm{y}\)-axis and whose length of latus rectum is the distance of the point \((2,-3)\) form the line \(3 x+4 y=5\), is given by :JEE Mains 2021 Hard
- Let \(\quad S=109+\frac{108}{5}+\frac{107}{5^2}+\ldots \ldots . .+\frac{2}{5^{107}}+\frac{1}{5^{108}}\). Then the value of \(\left(16 S -(25)^{-34}\right)\) is equal to \(............\).JEE Mains 2023 Hard
- Let \({a_1},{a_2},\;.\;.\;.\;.,{a_{49}}\) be in \(A.P.\) such that \(\mathop \sum \limits_{k = 0}^{12} {a_{4k + 1}} = 416\) and \({a_9} + {a_{43}} = 66\). If \(a_1^2 + a_2^2 + \ldots + a_{17}^2 = 140m,\) then \(m = \;\;..\;.\;.\;.\;\)JEE Mains 2018 Hard
- If the system of linear equations \(x+y+3 z=0\) \(x+3 y+k^{2} z=0\) \(3 x+y+3 z=0\) has a non-zero solution \((x, y, z)\) for some \(k \in R ,\) then \(x +\left(\frac{ y }{ z }\right)\) is equal toJEE Mains 2020 Medium
- Box \(I\) contains \(30\) cards numbered \(1\) to \(30\) and Box \(II\) contains \(20\) cards numbered \(31\) to \(50 .\) A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box \(I\) isJEE Mains 2020 Hard
- Let \(P (-2,-1,1)\) and \(Q \left(\frac{56}{17}, \frac{43}{17}, \frac{111}{17}\right)\) be the vertices of the rhombus PRQS. If the direction ratios of the diagonal \(RS\) are \(\alpha,-1, \beta\), where both \(\alpha\) and \(\beta\) are integers of minimum absolute values, then \(\alpha^{2}+\beta^{2}\) is equal to \(.....\)JEE Mains 2022 Hard