If w is the vector [2,-3,1] onto [1,2,5], find the components of w

Answer 1

To find the components of vector w onto vector [1,2,5], we can use the formula:

proj_v(w) = ((w • v) / (v • v)) * v

where • represents the dot product of two vectors.

Step 1: Calculate the dot product (w • v):
w • v = 2*1 + (-3)*2 + 1*5 = 2 - 6 + 5 = 1

Step 2: Calculate the dot product (v • v):
v • v = 1*1 + 2*2 + 5*5 = 1 + 4 + 25 = 30

Step 3: Divide the dot product of w and v by the dot product of v and v:
(1/30) * [1,2,5] = [(1/30) * 1, (1/30) * 2, (1/30) * 5]
= [1/30, 1/15, 1/6]

So, the components of w onto [1,2,5] are [1/30, 1/15, 1/6].