Question

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Find the angle θ between u = <7, –2> and v = <–1, 2>.
47.5°
42.5°
132.5°
137.5°

Answer 1

Explanation:

Cos θ = u*v

IuI *IvI

u * v = 7*(-1) + (-2)*2

= -7 - 4

= -11

IuI =
`\sqrt{7^(2)+(-2)^(2)}\\`

=
`√(49+4)\\\\`

=
`√(53)`

I vI =
`\sqrt{(-1)^(2)+2^(2)}\\`

=
`√(1+4)\\\\`

=
`√(5)\\`

Cos θ =
`(-11)/(√(53)*√(5) ) \\\\`

=
`(-11)/(16.28)\\\\`

Cos θ = -0.68

θ = 132.5°