Mathematics · 2017
JEE Main · 9 April 2017, Shift 1 · Q84
If the vector b =3 j +4 k is written as the sum of a vector b_1, parallel to a = i + j and a vector b_2, perpendicular to a, then b_1 × b_2 is equal…
If the vector $\displaystyle \overrightarrow{\mathrm{b}}=3 \hat{j}+4 \hat{k}$ is written as the sum of a vector $\displaystyle \overrightarrow{b_1}$, parallel to $\displaystyle \vec{a}=\hat{i}+\hat{j}$ and a vector $\displaystyle \overrightarrow{b_2}$, perpendicular to $\displaystyle \vec{a}$, then $\displaystyle \overrightarrow{b_1} \times \overrightarrow{b_2}$ is equal to :
Official answer
(2)
$\displaystyle 6 \hat{i}-6 \hat{j}+\frac{9}{2} \hat{k}$
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=3 i+2 j+2 k and b= i+2 j-2 k be two vectors. If a vector perpendicular to both the vectors a+ b and a- b has the magnitude 12 then one such…2019
JEE Main 2017 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.