JEE Mains · Maths · STD 12 - 10. vector algebra
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 ...... .
- A \(452\)
- B \(396\)
- C \(486\)
- D \(512\)
Answer & Solution
Correct Answer
(C) \(486\)
Step-by-step Solution
Detailed explanation
Let \(\overrightarrow{ x }=\lambda \overrightarrow{ a }+\mu \overrightarrow{ b } \quad(\lambda\) and \(\mu\) are scalars) \(\overrightarrow{ x }=\hat{ i }(2 \lambda+\mu)+\hat{ j }(2 \mu-\lambda)+\hat{ k }(\lambda-\mu)\) Since…
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
- Number of solutions of \( \sqrt{3}\cos 2\theta+8\cos \theta+3\sqrt{3}=0 \), \( \theta \in [-3\pi, 2\pi] \) is:JEE Mains 2026 Hard
- Let \(\vec{a}, \vec{b}\) and \(\vec{c}\) be three non zero vectors such that \(\vec{b} \cdot \vec{c}=0\) and \(\vec{a} \times(\vec{b} \times \vec{c})=\frac{\vec{b}-\vec{c}}{2}\). If \(\vec{d}\) be a vector such that \(\vec{b} \cdot \vec{d}=\vec{a} \cdot \vec{b}\), then \((\vec{a} \times \vec{b}) \cdot(\vec{c} \times \vec{d})\) is equal toJEE Mains 2023 Medium
- Let \(\alpha, \beta \in \mathrm{N}\) be roots of equation \(\mathrm{x}^2-70 \mathrm{x}+\lambda=0\), where \(\frac{\lambda}{2}, \frac{\lambda}{3} \notin \mathrm{N}\). If \(\lambda\) assumes the minimum possible value, then \(\frac{(\sqrt{\alpha-1}+\sqrt{\beta-1})(\lambda+35)}{|\alpha-\beta|}\) is equal to :JEE Mains 2024 Hard
- For \(0 \le x \le \frac{\pi }{2}\), the value of \(\int\limits_0^{{{\sin }^2}\,x} {{{\sin }^{ - 1}}\,\left( {\sqrt t } \right)} dt + \int\limits_0^{{{\cos }^2}\,x} {{{\cos }^{ - 1}}\,\left( {\sqrt t } \right)}\, dt\) equalsJEE Mains 2013 Hard
- The value of the definite integral \(\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{d x}{\left(1+e^{x \cos x}\right)\left(\sin ^{4} x+\cos ^{4} x\right)}\) is equal to:JEE Mains 2021 Hard
- If \(A = \left[ {\begin{array}{*{20}{c}}2&{ - 3}\\{ - 4}&1\end{array}} \right],\) then \(adj\;\left( {3{A^2} + 12A} \right) = \) . . . .JEE Mains 2017 Medium
More PYQs from JEE Mains
- If the Rolle's theorem holds for the function \(f(x) = 2x^3 + ax^2 + bx\) in the interval \([-1, 1 ]\) for the point \(c = \frac{1}{2}\) , then the value of \(2a + b\) isJEE Mains 2015 Hard
- Consider the quadratic equation \(\left( {c - 5} \right)\,{x^2} - 2cs + \left( {c - 4} \right) = 0\), \(c \ne 5\). Let \(S\) be the set of all integral values of \(c\) for which one root of the equation lies in the interval \((0, 2)\) and its other root lies in the interval \((2, 3)\). Then the number of elements in \(S\) isJEE Mains 2019 Hard
- If for \(\theta \in\left[-\frac{\pi}{3}, 0\right]\), the points \((x, y)=\left(3 \tan \left(\theta+\frac{\pi}{3}\right), 2 \tan \left(\theta+\frac{\pi}{6}\right)\right)\) lie on \(x y+\alpha x+\beta y+\gamma=0\), then \(\alpha^2+\beta^2+\gamma^2\) is equal to :JEE Mains 2025 Medium
- The number of ways in which an examiner can assign \(30\) marks to \(8\) questions, giving not less than \(2\) marks to any question, isJEE Mains 2013 Hard
- Suppose that the points \((h, k), (1, 2)\) and \((-3, 4)\) lie on the line \(L_1\). If a line \(L_2\) passing through the points \((h, k)\) and \((4, 3)\) is perpendicular to \(L_1\), then \(\frac{k}{h}\) equalsJEE Mains 2019 Hard
- From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is :JEE Mains 2026 Easy