Question

Can someone start me off on these and please explain step by step how you got everything because I'm having difficulty understanding the entire concept.

Find the projection of u onto v and calculate its magnitude.

a) u = (2,5) v = (6,4)
b) u = (3, 6, -2) v = (-4, 3, 8)

2) If u and v are non zero vectors, but Projection (u unto v) = 0, what conclusion can be drawn?
Would that also mean Projection (v unto u) = 0?

3) Find the projection of PQ onto each of the coordinate axes, where point (2,3,5) and Q is the point (-1,2,5).

Answer 1

The projection of vector u onto vector v is defined as
(u∙v)/│v│

u∙v = (2,5)∙(6,4) = 12+20 = 32
│v│ = √(6^2+4^2) = √52

so the projection of u onto v
= 32/√52 = 16/√13

follow this method for the other questions.

Think of the "projection of u onto v" as the 'shadow' cast by u onto v by a light from above shining perpendicular to v.

So if u does not cast a shadow on v, (the projection is zero), what should that tell you about the direction of u in relation to v ??