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# Determine the angle measure between vectors u and v?

U=4i-2j and v=i+3j

### 3 Answers

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- la consoleLv 76 years agoFavorite Answer
u = 4i - 2j

tan(u) = - 2/4 = - 1/2 → angle_u = - 26.565°

v = i + 3j

tan(v) = 3/1 = 3 → angle_v = 71.565°

angle between u and v:

= 71.565 - (- 26.565)

= 71.565 + 26.565

= 98.130°

- Wayne DeguManLv 76 years ago
u.v = |u||v|cosθ

Now, u.v => (4)(1) + (-2)(3) = -2

|u| = √(4² + 2²) => √20

|v| = √(1² + 3²) => √10

so, -2 = √20√10 x cosθ

=> cosθ = -2/√200

so, θ = cos⁻¹(-2/√200) => 98.1°

:)>

- lia lLv 56 years ago
u=4i-2j and v=i+3j

cos (angle between u and v)=

(4i-2j )(i+3j )/length(u)*length(v)

length(u)=sqrt(4^2+2^2)=sqrt20=2sqrt5

length(v)=sqrt(1+3^2)=sqrt10=sqrt2*sqrt5

cos (angle between u and v)

=(4-6)/10sqrt2=-1/5sqrt2

angle between u and v )=

acos(-1/5sqrt2)=1.7

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