Question

Find the projection of the vector $\hat i-\hat j$ on the vector $\hat i+\hat j$

Answer 1

Let the two vector be a and b.

Then,

a = i - j and b = i + j

We need to find the projection of a on b.

Therefore, Projection = |a.b|/|b|

Now, |a.b| = (1 × 1) + (-1 × 1) = 1 - 1 = 0

|b| = √(1)² + (1)² = √2

∴ Projection = 0/√2 = 0

Hence, the projection of a on b is zero.

Hope it helps.