<p>The projection of the vector $\vec{i} - \vec{j}$ on the vector $\vec{i} + \vec{j}$ is</p>
Step-by-Step Solution
Key Concept: Use the dot product formula for projection: projection of vector a on b equals (a·b)/|b|.
Solution: Let $\vec{a} = \hat{i} - \hat{j}$ and $\vec{b} = \hat{i} + \hat{j}$ Projection of $\vec{a}$ on $\vec{b}$ is given by: $\text{Projection} = \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|} = \frac{(\hat{i} - \hat{j}) \cdot (\hat{i} + \hat{j})}{\sqrt{1^2 + 1^2}} = \frac{1 \cdot 1 + (-1) \cdot 1}{\sqrt{2}} = \frac{1 - 1}{\sqrt{2}} = 0$ Hence, the projection of vector $\vec{a}$ on $\vec{b}$ is 0.
Correct Answer: a