AIEEE 2008 (Offline)Question 1
The vector $\vec a=\alpha\hat i+2\hat j+\beta\hat k$ lies in the plane of the vectors $\vec b=\hat i+\hat j$ and $\vec c=\hat j+\hat k$ and bisects the angle between $\vec b$ and $\vec c$. Then which one of the following gives possible values of $\alpha$ and $\beta$?
Vector Algebra
Solution
The bisector is along $\hat b+\hat c=\frac1{\sqrt2}(1,2,1)$; with $j$-component $2$, $\vec a=\hat i+2\hat j+\hat k$, so $\alpha=\beta=1$.