Hi! So I asked about this question earlier and I've been trying to solve it with the directions I was given by someone before, but, I'm still confused and keep getting weird numbers. Can someone help me with this?
Directions: Find the angle, θ, between the vectors. If needed, round your answer to the nearest tenth.
u = <3, 2>
v = <4, 0>
recall the dot product
u•v = |u||v|cosθ
3*4 + 2*0 = √13 * 4 *cosθ
cosθ = 12 / 4√13
θ = 33.7°
Or, you could notice that v is just along the x-axis, so
tanθ = 2/3
θ = 33.7
Of course, I'd be happy to help you with that! To find the angle, θ, between two vectors, you can use the formula:
θ = arccos((u · v) / (|u| * |v|))
where u · v represents the dot product of the vectors, and |u| and |v| represent the magnitudes of the vectors.
Let's calculate step by step:
1. Calculate the dot product of vectors u and v:
u · v = (3 * 4) + (2 * 0)
= 12 + 0
= 12
2. Calculate the magnitudes of vectors u and v:
|u| = √(3^2 + 2^2)
= √(9 + 4)
= √13
|v| = √(4^2 + 0^2)
= √16
= 4
3. Plug in the values into the formula:
θ = arccos(12 / (√13 * 4))
4. Use a calculator to find the arccosine of the result:
θ ≈ arccos(12 / (√13 * 4))
θ ≈ arccos(12 / (4 * √13))
θ ≈ arccos(12 / (4 * 3.60555128))
θ ≈ arccos(12 / 14.42220512)
θ ≈ arccos(0.831)
θ ≈ 0.586 radians (rounded to the nearest tenth)
So, the angle θ between the vectors u = <3, 2> and v = <4, 0> is approximately 0.586 radians.