Use the geometric description in Theorem 1 to prove Theorem 2 (iii): v w = 0
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Use the geometric description in Theorem 1 to prove Theorem 2 (iii): v × w = 0 if and only if w = λv for some scalar λ or v = 0.
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THEOREM 1 Geometric Description of the Cross Product Given two nonzero non- parallel vectors v and w with angle between them, the cross product v x w is the unique vector with the following three properties: (i) vx wis orthogonal to v and w. (ii) v x w has length ||v||||w|| sin 8. (iii) {v, w, vx w} forms a right-handed system.
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vxw 0 if and only if vxw 0 that is using Theorem 2 b if and only if vw sin 0 0 where i...View the full answer
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