Determine the projection of the vector v = (−1, 6, 4) onto the vector u = (−1, 2, 4).
Projection is the dot product (if you have the angle), or in component format
projection- (-1*-1)+(6*2)+(4*4)
= 1+12+16=29
Yeah I understand that part, but what about projection onto vector u?
to project v onto u, just do
v • u/|u|
= 29/√21
If you want that in vector form, just multiply
29 * u/√21 = (-29/√21,58/√21,116/√21)
To determine the projection of the vector v onto the vector u, you can use the formula:
proj_u(v) = (v ⋅ u) / ||u||^2 * u
where v ⋅ u represents the dot product of v and u, ||u||^2 denotes the magnitude of u squared, and "*" represents scalar multiplication.
1. Calculate the dot product of v and u:
(v ⋅ u) = (-1)(-1) + (6)(2) + (4)(4) = 1 + 12 + 16 = 29
2. Calculate the magnitude of u squared:
||u||^2 = (-1)^2 + (2)^2 + (4)^2 = 1 + 4 + 16 = 21
3. Calculate the projection:
proj_u(v) = (29 / 21) * (-1, 2, 4)
= (-29/21, 58/21, 116/21)
Therefore, the projection of the vector v onto the vector u is (-29/21, 58/21, 116/21).