Question

Find the projection of vector \((\hat i-\hat j)\) on vector \((\hat i+\hat j)\).

Hint:

Projection formula \(=\dfrac{\vec a\cdot\vec b}{|\vec b|}\); here the dot product is zero.

Answer 1

Step 1: Geometric shortcut:
\(\hat i-\hat j\) and \(\hat i+\hat j\) are perpendicular: their dot product is \(1-1=0\), so the angle between them is \(90^\circ\).

Step 2: Consequence for projection:
The projection of one vector on a perpendicular vector is always \(|\vec a|\cos 90^\circ=0\).

Final Answer:
Hence the projection is \(\boxed{0}\).