JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\overrightarrow{a}=2 \hat{i}-\hat{j}+\hat{k}\) and \(\overrightarrow{b}=\lambda \hat{j}+2 \hat{k}, \lambda \in Z\) be two vectors, Let \(\overrightarrow{ c }=\overrightarrow{ a } \times \overrightarrow{ b }\) and \(\overrightarrow{ d }\) be a vector of magnitude 2 in yz-plane. If \(|\overrightarrow{ c |}=\sqrt{53}\), then the maximum possible value of \((\overrightarrow{ c } \cdot \overrightarrow{ d })^2\) is equal to :
- A 26
- B 104
- C 208
- D 52
Answer & Solution
Correct Answer
(C) 208
Step-by-step Solution
Detailed explanation
\(\overrightarrow{a}=2 \hat{i}-\hat{j}+\hat{k}\) \(\overrightarrow{ b }=\lambda \hat{ j }+2 \hat{ k } ; \lambda \in Z\) \(\overrightarrow{ c }=\overrightarrow{ a } \times \overrightarrow{ b }=(-2-\lambda) \hat{ i }-4 \hat{ j }+2 \lambda \hat{ k }\)…
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
- If the area of the region bounded by the curves \(y=4-\frac{x^2}{4}\) and \(y=\frac{x-4}{2}\) is equal to \(\alpha\), then \(6 \alpha\) equalsJEE Mains 2025 Medium
- If \(\int {{x^5}\,{e^{ - {x^2}}}\,dx\, = \,g\,(x)\,{e^{ - {x^2}}} + \,c,} \) where \(c\) is a constant of integration, then \(g(-1)\) is equal toJEE Mains 2019 Hard
- The integral \(\int {\frac{{dx}}{{{{(x + 1)}^{\frac{3}{4}}}{{(x - 2)}^{\frac{5}{4}}}}}} \) is equal toJEE Mains 2015 Hard
- If \(\mathrm{p}\) and \(\mathrm{q}\) are the lengths of the perpendiculars from the origin on the lines, \(x \operatorname{cosec} \alpha-y \sec \alpha=\operatorname{kcot} 2 \alpha\) and \(x \sin \alpha+y \cos \alpha=k \sin 2 \alpha\) respectively, then \(\mathrm{k}^{2}\) is equal to :JEE Mains 2021 Hard
- Let \(f(x)=\left\{\begin{array}{l}x-1, x \text { is even, } \\ 2 x, x \text { is odd, }\end{array}\right.\). If for some \(a \in N, f(f(f(a)))=21\), then \(\lim _{x \rightarrow a^{-}}\left\{\frac{|x|^3}{a}-\left[\frac{x}{a}\right]\right\}\), where \([t]\) denotes the greatest integer less than or equal to \(t\), is equal to :JEE Mains 2024 Hard
- Let \(S = \{1, 2, 3, ….., 100\}\). The number of non-empty subsets \(A\) of \(S\) such that the product of elements in \(A\) is even isJEE Mains 2019 Hard
More PYQs from JEE Mains
- Let \(y=y(x)\) be the solution of the differential equation \(e^{x} \sqrt{1-y^{2}} d x+\left(\frac{y}{x}\right) d y=0, y(1)=-1\) Then the value of \((y(3))^{2}\) is equal to:JEE Mains 2021 Hard
- The difference between degree and order of a differential equation that represents the family of curves given by \(y^{2}=a\left(x+\frac{\sqrt{a}}{2}\right), a>0\) isJEE Mains 2021 Medium
- The mean age of \(25\) teachers in a school is \(40\, years\). A teacher retires at the age of \(60\, years\) and a new teacher is appointed in his place. If now the mean age of the teachers in this school is \(39\, years\), then the age (in years) of the newly appointed teacher isJEE Mains 2017 Medium
- If the term without \(x\) in the expansion of \(\left( x ^{\frac{2}{3}}+\frac{\alpha}{ x ^3}\right)^{22}\) is \(7315\) , then \(|\alpha|\) is equal to \(...........\).JEE Mains 2023 Hard
- Let \(\left\{a_{n}\right\}_{n=0}^{\infty}\) be a sequence such that \(a_{0}=a_{1}=0\) and \(a_{ n +2}=3 a_{ n +1}-2 a_{ n }+1, \forall n \geq 0\).Then \(a_{25} a_{23}-2 a_{25} a_{22}-2 a_{23} a_{24}+4 a_{22} a_{24}\) is equal to.JEE Mains 2022 Hard
- Let \(f, g: N -\{1\} \rightarrow N\) be functions defined by \(f(a)=\alpha\), where \(\alpha\) is the maximum of the powers of those primes \(p\) such that \(p^{\alpha}\) divides \(a\), and \(g(a)=a+1\), for all \(a \in N -\{1\}\). Then, the function \(f+ g\) is.JEE Mains 2022 Hard