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  4. The component of vector vecA=2 hati+3 hatj along the direction of ( hati- hatj) is

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Q. The component of vector $\vec{A}=2\hat{i}+3\hat{j}$ along the direction of $\left(\hat{i}-\hat{j}\right)$ is

Motion in a Plane

Solution:

Given : $\vec{A}=2\hat{i}+3\hat{j}$,
$\vec{B}=2\hat{i}-\hat{j}$ (say)
Component of $\vec{A}$ along the direction of $\vec{B}$
$=\frac{\vec{A}\cdot\vec{B}}{B}$
$=\frac{\left(2\hat{i}+3\hat{j}\right)\cdot\left( \hat{i} - \hat{j}\right)}{\sqrt{2}}$
$=-\frac{1}{\sqrt{2}}$