# Find the angle between u and v.?

Find the angle between u and v. Let u = (3,-2,1) and v = (2,-3,1)

### 3 Answers

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- mohanrao dLv 79 years agoBest Answer
u = <3, -2, 1 > and v = <2, -3, 1

II u II = √(9+4+1) = √14

II v II = √(4+9+1) = √14

θ = cos^-1 [ u.v / II u II II v II ]

= cos^-1 [(3*2 + (-2*-3) + (1*1)) /14 ]

= cos^-1(13/14)

= 21.79°

- 9 years ago
a * b = |a| |b| cosθ

<3, -2, 1> * <2, -3, 1> = sqrt(1^2 + 2^2 + 3^2) * sqrt(1^2 + 2^2 + 3^2) * cosθ

6 + 6 + 1 = 14 * cosθ

13/14 = cosθ

θ = arccos(13/14)

θ = 0.380 rad

θ = 21.79 deg

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