Question: Question 5: 5 Marks Consider the vectors ~u = < -2, 2, -3 >, ~v = < -1, 3, -4 >, w~ = < 2,

Question 5: 5 Marks

Consider the vectors ~u =< -2, 2, -3 >, ~v =< -1, 3, -4 >, w~ =< 2, -6, 2 > and the points A(2, 6, -1) and B(-3, -5, 7).

Evaluate

(5.1) The distance between the two points.

(5.2) ||2~u - 3~v + 1 2w~||

(5.3) The unit vector in the direction of w~ .

(5.4) Suppose ~u; ~v and w~ are vectors in 3D, where ~u = (u1, u2, u3) ; ~v = (v1, v2, v3) and w~ = (w1, w2, w3).

Express (~u ~v) w~ as a determinant.

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