The cross product between vectors in R3 is defined by the formula

Where

(a) Show that u = v × w is orthogonal, under the dot product, to both v and w.
(b) Show that v × w = 0 if and only if v and w are parallel.
(c) Prove that if v, w ˆŠ R3 are orthogonal nonzero vectors, then u = v × w. v. w form an orthogonal basis of R3.
(d) True or false: If v, w ˆŠ R3 are orthogonal unit vectors, then v, w and u = v × w form an orthonormal basis of R3.

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(5.2) 01 W3