What is the best approximation of the projection of (5, - 1) onto (2, 6)

The answer is 0.10 (2,6)

0.1 (2, 6) = (0.2, 0.6)

Step-by-step explanation:

The projection of B onto A will be ...

|B|·cos (θ) * uA

where uA = A/|A|, a unit vector in the A direction.

The dot product of A and B is ...

A•B = |A|·|B|·cos (θ), so the desired vector is ...

projection of B onto A = (A•B) / |A|· (A/|A|) = A· (A•B) / |A|²

For A = (2,6) and B = (5, - 1), this is ...

projection of (5, - 1) onto (2, 6) = (2, 6) · (2·5-6·1) / (2²+6²) = (2, 6) ·4/40 = 0.1· (2, 6)

= (0.2, 0.6)