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Question

Let u, v and w be vectors such u +v +w =0 . If u =3, v =4 and w =5, then find u ·v +v ·w +w ·u .

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Solution

Given thatu+v+w=0u+v+w=0u+v+w2=0u2+v2+w2+2u. v+v. w+w. u=032+42+52+2u. v+v. w+w. u=0 (Given:u=3, v=4 and w=5)9+16+25+2u. v+v. w+w. u=050+2u. v+v. w+w. u=02u. v+v. w+w. u=-50 u. v+v. w+w. u=-502=-25

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