Find the projection of the vector $ˆ i - ˆ j$ on the vector $ˆ i + ˆ j$ .

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Solution

Let $\to a = ˆ i - ˆ j$
$\to b = ˆ i + ˆ j$
Now, projection of vector $\to a$ on $\to b$ is
$\frac{1}{| \to b |} (\to a . \to b) = \frac{1}{\sqrt{1 + 1}} (1 - 1) = 0$

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