Find the component of vector vec{r} in the di | vedclass

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(A) The component of a vector $\vec{r}$ in the direction of another vector $\vec{a}$ is given by the projection of $\vec{r}$ onto $\vec{a}$.This is a

Vedclass · Accepted Answer

$\frac{(\vec{r} \cdot \vec{a}) \vec{a}}{a^2}$

Vedclass · Answer

(A) The component of a vector $\vec{r}$ in the direction of another vector $\vec{a}$ is given by the projection of $\vec{r}$ onto $\vec{a}$.This is a vector quantity defined as the projection vector.The formula for the projection of $\vec{r}$ onto $\vec{a}$ is given by:$	ext{Component} = (\vec{r} \cdot \hat{a}) \hat{a}$Since the unit vector $\hat{a} = \frac{\vec{a}}{a}$,we substitute this into the formula:$	ext{Component} = \left( \vec{r} \cdot \frac{\vec{a}}{a} ight) \frac{\vec{a}}{a}$$	ext{Component} = \frac{(\vec{r} \cdot \vec{a}) \vec{a}}{a^2}$Thus,the correct option is $A$.

Find the component of vector $\vec{r}$ in the direction of vector $\vec{a}$.

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