Question

Find the projection of the vector $\hat i-3\hat j+7 \hat k$ on the vector $7\hat i-\hat j+8 \hat k$.

Answer 1

Let the two vector be a and b.

Then,

a = i - 3j + 7k and b = 7i - j  + 8k

We need to find the projection of a on b.

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

Now, |a.b| = (1 × 7) + (-3 × -1) + (7 × 8)

= 7 + 3 + 56

= 66

|b| = √[(7)² + (1)² + (8)²]

|b| = √114

∴ Projection = 66/√114

Hence, the projection of a on b is 66/√114.

Hope it helps.