Find the angle between the vectors u and v if $\mathbf { u } = \langle 3,4 \rangle$ ,and $\mathbf { v } = \langle - 1 , - 2 \rangle$ Round answer to two decimal places.
A)167.77°
B)168.46°
C)169.70°
D)170.66°
E)171.11°

Question

Quizplus · Accepted Answer

To find the angle between two vectors u and v, we use the dot product formula:
u · v = |u| |v| cosθ
where θ is the angle between u and v.
Using the given vectors, we have:
u · v = (11)(-7) + (14)(-9) + (9)(-10) = -261
|u| = sqrt(121 + 196 + 81) = sqrt(398)
|v| = sqrt(16 + 121 + 100) = sqrt(237)
So, we can solve for cosθ:
-261 = sqrt(398) sqrt(237) cosθ
cosθ = -261 / (sqrt(398) sqrt(237)) ≈ -0.997
Taking the inverse cosine, we get:
θ ≈ 169.70°
So, the best choice is C) 169.70°.

Find the Angle Between the Vectors U and V If u=⟨3,4⟩\mathbf { u } = \langle 3,4 \rangleu=⟨3,4⟩

Find the Angle Between the Vectors U and V If $\mathbf { u } = \langle 3,4 \rangle$