JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=3 \hat{i}+\hat{j}-\hat{k}\) and \(\vec{c}\) be three vectors such that \(\vec{c}\) is coplanar with \(\vec{a}\) and \(\vec{b}\). If the vector \(\vec{C}\) is perpendicular to \(\vec{b}\) and \(\vec{a} \cdot \vec{c}=5\), then \(|\vec{c}|\) is equal to
- A \(\sqrt{\frac{11}{6}}\)
- B \(\frac{1}{3 \sqrt{2}}\)
- C \(16\)
- D \(18\)
Answer & Solution
Correct Answer
(A) \(\sqrt{\frac{11}{6}}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \overrightarrow{\mathrm{c}}=\lambda(\overrightarrow{\mathrm{b}} \times(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}})) \\ & =\lambda((\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{b}})…
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 \(y=y(x)\) be the solution of the differential equation \(\left(1+x^2\right) \frac{d y}{d x}+y=e^{\tan ^{-1} x}, y(1)=0\). Then \(\mathrm{y}(0)\) isJEE Mains 2024 Hard
- Let the coefficients of the middle terms in the expansion of \(\left(\frac{1}{\sqrt{6}}+\beta x\right)^{4},(1-3 \beta x)^{2}\) and \(\left(1-\frac{\beta}{2} x\right)^{6}, \beta>0\), respectively form the first three terms of an \(A.P.\) If \(d\) is the common difference of this \(A.P.\), then \(50-\frac{2 d}{\beta^{2}}\) is equal to.JEE Mains 2022 Hard
- Let \(a_{1}, a_{2} \ldots, a_{n}\) be a given \(A.P.\) whose common difference is an integer and \(S _{ n }= a _{1}+ a _{2}+\ldots+ a _{ n }\) If \(a_{1}=1, a_{n}=300\) and \(15 \leq n \leq 50,\) then the ordered pair \(\left( S _{ n -4}, a _{ n -4}\right)\) is equal toJEE Mains 2020 Hard
- The range of \(a \in R\) for which the function \( f(x)=(4 a-3)\left(x+\log _{e} 5\right)+2(a-7) \cot \left(\frac{x}{2}\right) \sin ^{2}\left(\frac{x}{2}\right)\) \(x \neq 2 n \pi, n \in N ,\) has critical points, isJEE Mains 2021 Hard
- If \(\lim _{x \rightarrow 0} \frac{ ae ^{x}- b \cos x + ce ^{- x }}{ x \sin x }=2,\) then \(a + b + c\) is equal to ...........JEE Mains 2021 Hard
- If the system of linear equations
\(\begin{aligned} & 3 x+y+\beta z=3 \\ & 2 x+\alpha y-z=-3 \\ & x+2 y+z=4\end{aligned}\)
has infinitely many solutions, then the value of \(22 \beta-9 \alpha\) is :JEE Mains 2025 Easy
More PYQs from JEE Mains
- If a curve the \(y = f(x)\) passes through point \((1, -1)\) and satisfies the differential equation \(y\left( {1 + xy} \right)dx = xdy\) then \(f\left( { - \frac{1}{2}} \right) = \) . . . . .JEE Mains 2016 Hard
- Let \(A=\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & 4 & -1 \\ 0 & 12 & -3\end{array}\right)\). Then the sum of the diagonal elements of the matrix \(( A + I )^{11}\) is equal to:JEE Mains 2023 Hard
- lf a line \(L\) is perpendicular to the line \(5x - y\,= 1\) , and the area of the triangle formed by the line \(L\) and the coordinate axes is \(5\), then the distance of line \(L\) from the line \(x + 5y\, = 0\) isJEE Mains 2014 Hard
- 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 toJEE Mains 2024 Medium
- Let \(f(x)=\int \frac{d x}{\left(3+4 x^2\right) \sqrt{4-3 x^2}},|x| < \frac{2}{\sqrt{3}}\). If \(f(0)=0\) and \(f(1)=\frac{1}{\alpha \beta} \tan ^{-1}\left(\frac{\alpha}{\beta}\right), \alpha, \beta > 0\), then \(\alpha^2+\beta^2\) is equal to \(.........\).JEE Mains 2023 Hard
- If \(\lim _{x \rightarrow 0} \frac{3+\alpha \sin x+\beta \cos x+\log _e(1-x)}{3 \tan ^2 x}=\frac{1}{3}\), then \(2 \alpha-\beta\) is equal to :JEE Mains 2024 Hard