Question #213695

Determine whether ~u and ~v are orthogonal vectors, make an acute or obtuse angle: (1.1) ~u =< 1, 3, −2 >, ~v =< −5, 3, 2 >. (2) (1.2) ~u =< 1, −2, 4 >, ~v =< 5, 3, 7 >.


1
Expert's answer
2021-07-20T17:22:17-0400

1.1

u=(1,3,2),v=(5,3,2)uv=5+94=0u=(1,3,-2), v=(-5,3,2)\\ uv=-5+9-4=0\\

u orthogonal v


1.2

u=(1,2,4),v=(5,3,7)uv=56+28=27>0u=(1,-2,4), v=(5,3,7)\\ uv=5-6+28=27>0

u is not orthogonal v

u=1+4+16=21v=25+9+49=83cosϕ=uvuv=272183>0||u||=\sqrt{1+4+16}=\sqrt{21}\\ ||v||=\sqrt{25+9+49}=\sqrt{83}\\ \cos\phi=\frac{uv}{||u||\cdot||v||}=\frac{27}{\sqrt{21}\cdot\sqrt{83}}>0

acute angle


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