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  4. What will be the projection of vector vecA= hati+ hatj+ hatk on vector vecB= hati+ hatj ?

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Q. What will be the projection of vector $\vec{A}=\hat{i}+\hat{j}+\hat{k}$ on vector $\vec{B}=\hat{i}+\hat{j} ?$

JEE MainJEE Main 2021Motion in a Plane

Solution:

$(A \cos \theta) \hat{B}=A\left(\frac{\vec{A} \cdot \vec{B}}{A B}\right) \hat{B}=\frac{\vec{A} \cdot \vec{B}}{B} \hat{B}$
$=\frac{2}{\sqrt{2}}\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)=\hat{i}+\hat{j}$