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) 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.
(5.1)
(5.2)
(5.3)
(5.4)
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