Question

5. Le tv=〈1,1,1〉 and w=2i+j−3k.

(a) Calculate the following.

(i) 4v + 3w

(ii) ∥w∥

(iii) ew (i.e., the unit vector in the direction of w)

(iv) w·v

(v) cos(θ), where θ is the angle between w and v

(vi) projv(w) 3 (Forreference: v=〈1,1,1〉andw=2i+j−3k.)

(vii) The decomposition w = w|| + w⊥ with respect to v

(viii) w × v

(ix) sin(θ), where θ is the angle between v and w

(b) Are v and w orthogonal? Justify your answer! If not, determine whether the angle between them is acute or obtuse.

Answer 1