JEE Main 2021 (Online) 26th February Evening ShiftQuestion 1
If vectors $\vec{a}_1=x\hat{i}-\hat{j}+\hat{k}$ and $\vec{a}_2=\hat{i}+y\hat{j}+z\hat{k}$ are collinear, then a possible unit vector parallel to the vector $x\hat{i}+y\hat{j}+z\hat{k}$ is :
Vector Algebra
Solution
Collinear: $\vec a_1=k\vec a_2$, so $x=k$, $-1=ky$, $1=kz$. Hence $y=-\frac1k$, $z=\frac1k$. The vector $(x,y,z)=(k,-\frac1k,\frac1k)$. For $k=1$ it is $(1,-1,1)$ with unit vector $\frac1{\sqrt3}(\hat i-\hat j+\hat k)$. Option (B).