Find the angle between the vectors u and v if $\mathbf { u } = \mathbf { i } + 2 \mathbf { j }$ and $\mathbf { v } = 4 \mathbf { i } + 2 \mathbf { j }$ Round answer to two decimal places.
A)36.87°
B)37.83°
C)38.28°
D)34.94°
E)35.63°

Question

Quizplus · Accepted Answer

To find the angle between two vectors, we can use the dot product formula:

u · v = ||u|| ||v|| cosθ

where ||u|| and ||v|| are the magnitudes of the vectors, and θ is the angle between them.

First, we need to find the magnitudes of the vectors:

||u|| = √(1^2 + 2^2 + 5^2) = √30
||v|| = √(1^2 + 2^2 + 6^2) = √41

Next, we need to find the dot product of the vectors:

u · v = (1)(1) + (2)(2) + (5)(6) = 33

Now we can use the dot product formula to find the angle:

33 = √30 √41 cosθ
cosθ = 33 / (√30 √41)
θ ≈ 36.87°

Therefore, the answer is A) 36.87°.

Find the Angle Between the Vectors U and V If u=i+2j\mathbf { u } = \mathbf { i } + 2 \mathbf { j }u=i+2j

Find the Angle Between the Vectors U and V If $\mathbf { u } = \mathbf { i } + 2 \mathbf { j }$