Question
What is the projection of $\hat{\text{i}}+\hat{\text{j}}$ on $(\hat{\text{i}}-\hat{\text{j}})?$
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Answer
Let $\vec{\text{A}}=\hat{\text{i}}+\hat{\text{j}}$ and $\vec{\text{B}}=\hat{\text{i}}-\hat{\text{j}}$ Projection of $\vec{\text{A}}$ on $\vec{\text{B}}=|\vec{\text{A}}||\vec{\text{B}}|\cos\theta$ $\cos\theta=\frac{\vec{\text{A}}.\vec{\text{B}}}{|\vec{\text{A}}||\vec{\text{B}}|}=0$ $(\theta=90^\circ)$ $\theta=90^\circ,$ $\therefore$ Projection = 0.
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