Question

Let a = (2,5) and b = (2,1). Find the projection of b onto a.

Answer 1

To find the projection of b onto a, use the formula projab = (b · a / ||a||^2) · a, where · represents the dot product and ||a||^2 is the magnitude of a squared. Plug in the given values for a and b and calculate the dot product. Then, calculate the projection of b onto a using the formula.

Step-by-step explanation:

To find the projection of b onto a, we can use the formula:

projab = (b · a / ||a||2) · a

where · represents the dot product and ||a||2 is the magnitude of a squared.

Using the given values a = (2,5) and b = (2,1), we can calculate:

a · a = 2 · 2 + 5 · 5 = 29

b · a = 2 · 2 + 1 · 5 = 4 + 5 = 9

projab = (9 / 29) · (2,5) = (18/29, 45/29)