Question

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

Answer 1

Answer:

The answer is 0.10(2,6)

Step-by-step explanation:

Answer 2

Answer:

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)