The projection of i-j on the vector i+j is:

The correct answer is Option (4) → 0

Let $\vec a$ and $\vec b$ be two vectors.

Projection of $\vec a$ on $\vec b$ = $\frac{a.b}{|b|^2}\hat b$

$a=\hat i-\hat j$

$b=\hat i+\hat j$

then,

$a.b=1×1-1×1=0$

∴ Projection of $\vec a$ on $\vec b$ = 0