Mathematics · 2021
JEE Main · 22 July 2021, Shift 2 · Q72
Let three vectors a, b and c be such that a × b = c, b × c = a and | a |=2. Then which one of the following is not true?
Let three vectors $\displaystyle \vec{a}, \vec{b}$ and $\displaystyle \vec{c}$ be such that $\displaystyle \vec{a} \times \vec{b}=\vec{c}, \vec{b} \times \vec{c}=\vec{a}$ and $\displaystyle |\vec{a}|=2$. Then which one of the following is not true ?
Official answer
(3)
$\displaystyle |3 \vec{a}+\vec{b}-2 \vec{c}|^2=51$
More from Vectors
- Let a= i- j+2 k and let b be a vector such that a × b=2 i- k and a · b=3. Then the projection of b on the vector a- b is:2022
- Let S be the set of all a ∈ R for which the angle between the vectors u=a( log_e b) i-6 j+3 k and v=( log_e b) i+2 j+2 a( log_e b) k,(b>1) is acute.…2022
- If (2,3,9),(5,2,1),(1, λ, 8) and (λ, 2,3) are coplanar, then the product of all possible values of λ is:2022
- If (1,5,35),(7,5,5),(1, λ, 7) and (2 λ, 1,2) are coplanar, then the sum of all possible values of λ is:2021
- Let a= i+ j+ k, b=2 i+2 j+ k and d= a × b. If c is a vector such that a · c=| c|, | c-2 a|^2=8 and the angle between d and c is (π)/4, then |10-3 b ·…2025
- Let the volume of a parallelopiped whose coterminous edges are given by u= i+ j+λ k, v= i+ j+3 k and w=2 i+ j+ k be 1 cu. unit. If θ be the angle…2020
- Let a, b, c be three vectors mutually perpendicular to each other and have same magnitude. If a vector r satisfies a ×{( r- b) × a}+ b ×{( r- c) ×…2021
- Let a, b and c be distinct positive numbers. If the vectors a i+a j+c k, i+ k and c i+c j+b k are co-planar, then c is equal to:2021
JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.