JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}=4 \hat{i}-\hat{j}+\hat{k}, \vec{b}=11 \hat{i}-\hat{j}+\hat{k}\) and \(\vec{c}\) be a vector such that \((\vec{a}+\vec{b}) \times \vec{c}=\vec{c} \times(-2 \vec{a}+3 \vec{b}) \text {. }\) If \((2 \vec{a}+3 \vec{b}) \cdot \vec{c}=1670\), then \(|\vec{c}|^2\) is equal to :
- A \(1627\)
- B \(1618\)
- C \(1600\)
- D \(1609\)
Answer & Solution
Correct Answer
(B) \(1618\)
Step-by-step Solution
Detailed explanation
\( (\vec{a}+\vec{b}) \times \vec{c}-\vec{c} \times(-2 \vec{a}+3 \vec{b})=0 \) \( (\vec{a}+\vec{b}) \times \vec{c}+(-2 \vec{a}+3 \vec{b}) \times \vec{c}=0 \) \( \Rightarrow(\vec{a}+\vec{b})-2 \vec{a}+3 \vec{b}) \times \vec{c}=0 \)…
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
- Let \(S\) be the set of all \(a \in N\) such that the area of the triangle formed by the tangent at the point \(P ( b , c ), b , c \in N\), on the parabola \(y ^2=2 ax\) and the lines \(x=b, y=0\) is \(16\) unit \(^2\), then \(\sum_{\text {aes }} a\) is equal to \(..........\).JEE Mains 2023 Hard
- If \(S_1\) and \(S_2\) are respectively the sets of local minimum and local maximum points of the function. \(f(x) = 9{x^4} + 12{x^3} - 36{x^2} + 25,x \in R\), thenJEE Mains 2019 Hard
- Let \(A=\{-4,-3,-2,0,1,3,4\}\) and \(R =\{( a , b ) \in A\) \(\times A : b =| a |\) or \(\left.b ^2= a +1\right\}\) be a relation on \(A\). Then the minimum number of elements, that must be added to the relation \(R\) so that it becomes reflexive and symmetric, is \(........\).JEE Mains 2023 Medium
- The number of \(7\)-\(digit\) numbers which are multiples of \(11\) and are formed using all the digits \(1,2,3,4,5,7\) and \(9\) isJEE Mains 2022 Hard
- The number of common tangents, to the circles \(x^2+y^2-18 x-15 y+131=0\) and \(x^2+y^2-6 x-6 y-7=0\), is :JEE Mains 2023 Medium
More PYQs from JEE Mains
- Let \(x _{ i }(1 \leq i \leq 10)\) be ten observations of a random variable \(X .\) If \(\sum \limits_{ i =1}^{10}\left( x _{ i }- p \right)=3\) and \(\sum \limits_{ i =1}^{10}\left( x _{ i }- p \right)^{2}=9\) where \(0 \neq p \in R ,\) then the standard deviation of these observations isJEE Mains 2020 Medium
- If \(y =\sum \limits_{ k =1}^{6} k \cos ^{-1}\left\{\frac{3}{5} \cos k x -\frac{4}{5} \sin k x \right\}\) then \(\frac{ dy }{ dx }\) at \(x =0\) isJEE Mains 2020 Medium
- The distance of the point \((7,10,11)\) from the line \(\frac{x-4}{1}=\frac{y-4}{0}=\frac{z-2}{3}\) along the line \(\frac{x-9}{2}=\frac{y-13}{3}=\frac{z-17}{6}\) isJEE Mains 2025 Easy
- If \(2x = {y^{\frac{1}{5}}} + {y^{ - \frac{1}{5}}}\) and \((x^2 -1) \frac{{{d^2}y}}{{d{x^2}}} + \lambda x\frac{{dy}}{{dx}} + ky = 0\) , then \( \lambda + k\) is equal toJEE Mains 2017 Hard
- The sum of all possible values of \(\theta \in [0, 2\pi]\), for which the system of equations :
\(x\cos 3\theta - 8y - 12z = 0\)
\(x\cos 2\theta + 3y + 3z = 0\)
\(x + y + 3z = 0\)
has a non-trivial solution, is equal to :JEE Mains 2026 Hard - The number of four letter words that can be formed using the letters of the word \(BARRACK\) isJEE Mains 2018 Hard