First slide

Cross product of vectors or vector product of vectors

Question

If vectors $\vec{a} and \vec{b}$ are non-collinear, then $\frac{\vec{a}}{| \vec{a} |} + \frac{\vec{b}}{| \vec{b} |}$ is

Moderate

A

a unit vector
B

in the plane of $\vec{a} and \vec{b}$
C

equally inclined to $\vec{a} and \vec{b}$
D

perpendicular to $\vec{a} × \vec{b}$

Solution

Obviously, $\frac{\vec{a}}{| \vec{a} |} + \frac{\vec{b}}{| \vec{b} |}$ is a vector in the plane of $\vec{a} and \vec{b}$ and hence perpendicular to $\vec{a} × \vec{b}$
It is also equally inclined to $\vec{a} and \vec{b}$ as it is along the angle bisector.

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