Let overrightarrow{a} and overrightarrow{b} b | vedclass

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Question

(D) The projection of vector $\overrightarrow{a}$ on $\overrightarrow{b}$ is given by $\frac{\overrightarrow{a} \cdot \overrightarrow{b}}{|\overrighta

Vedclass · Accepted Answer

$\frac{2}{3}$

Vedclass · Answer

(D) The projection of vector $\overrightarrow{a}$ on $\overrightarrow{b}$ is given by $\frac{\overrightarrow{a} \cdot \overrightarrow{b}}{|\overrightarrow{b}|}$.The projection of vector $\overrightarrow{b}$ on $\overrightarrow{a}$ is given by $\frac{\overrightarrow{b} \cdot \overrightarrow{a}}{|\overrightarrow{a}|}$.The ratio of the projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ to the projection of $\overrightarrow{b}$ on $\overrightarrow{a}$ is:$\frac{\frac{\overrightarrow{a} \cdot \overrightarrow{b}}{|\overrightarrow{b}|}}{\frac{\overrightarrow{b} \cdot \overrightarrow{a}}{|\overrightarrow{a}|}} = \frac{\overrightarrow{a} \cdot \overrightarrow{b}}{|\overrightarrow{b}|} 	imes \frac{|\overrightarrow{a}|}{\overrightarrow{b} \cdot \overrightarrow{a}}$Since the dot product is commutative,$\overrightarrow{a} \cdot \overrightarrow{b} = \overrightarrow{b} \cdot \overrightarrow{a}$.Therefore,the ratio simplifies to $\frac{|\overrightarrow{a}|}{|\overrightarrow{b}|} = \frac{2}{3}$.

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two vectors such that $|\overrightarrow{a}| = 2$ and $|\overrightarrow{b}| = 3$. Then the ratio of the projection of $\overrightarrow{a}$ on $\overrightarrow{b}$ to that of $\overrightarrow{b}$ on $\overrightarrow{a}$ is:

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