Let V = R3(R) and let v1=[ -1 0 2]^T , v2 = [0 2 -3]^T and v3=[2 2 3]^T.

Question

Suppose that v4 is another vector which is orthogonal to v1 and v2, and satisfying v2.v4 = -3.

Calculate the following expressions:

(i) v1 . v2,

(ii) v3 . v4,

(iii) (2v1 + 3v2 - v3) . v4,

(iv)||v1|| , ||v2-v3||

(v) d(v1,v2), the distance between v1 and v2,

(vi) the angle between the vectors v1 and v2.

So in the question, it is given that "v4 is another vector which is orthogonal to v1 and v2, and satisfying v2.v4 = -3 ". But, if v4 is orthogonal to v2, shouldn't that mean v2.v4=v4.v2 =0?? But it is given v2.v4= -3

Or am I missing something?

Answer 1

I would say that maybe they meant v4.v3 = -3, but then they ask for v4.v3

So yes, I'd say something is amiss. Maybe they meant only that v4⊥v1.

Answer 2

Thank you!