If vec{a} and vec{b} are two non-collinear ve | vedclass

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Question

(A) Let $\hat{a} = \frac{\vec{a}}{|\vec{a}|}$ and $\hat{b} = \frac{\vec{b}}{|\vec{b}|}$ be the unit vectors along $\vec{a}$ and $\vec{b}$ respectively

Vedclass · Accepted Answer

a vector parallel to an angle bisector of $\vec{a}$ and $\vec{b}$

Vedclass · Answer

(A) Let $\hat{a} = \frac{\vec{a}}{|\vec{a}|}$ and $\hat{b} = \frac{\vec{b}}{|\vec{b}|}$ be the unit vectors along $\vec{a}$ and $\vec{b}$ respectively.Then,$|\vec{b}| \vec{a} + |\vec{a}| \vec{b} = |\vec{a}| |\vec{b}| \left( \frac{\vec{a}}{|\vec{a}|} + \frac{\vec{b}}{|\vec{b}|} \right) = |\vec{a}| |\vec{b}| (\hat{a} + \hat{b})$.Since $\hat{a} + \hat{b}$ is the diagonal of the rhombus formed by unit vectors $\hat{a}$ and $\hat{b}$,it represents the angle bisector of the angle between $\vec{a}$ and $\vec{b}$.Thus,$|\vec{b}| \vec{a} + |\vec{a}| \vec{b}$ is a vector parallel to the angle bisector of $\vec{a}$ and $\vec{b}$.

If $\vec{a}$ and $\vec{b}$ are two non-collinear vectors,then $|\vec{b}| \vec{a} + |\vec{a}| \vec{b}$ represents:

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