Let θ be the angle between two vectors v and u . If v*u =12, |v|=2, |u|=6√2 and 0∘<θ<180∘, what is the value of θ (in degrees)?
v•u = |v| |u| cosθ, so
cosθ = 12/(2*6√2) = 1/√2
clear now?
To find the value of θ, we can use the dot product formula:
v * u = |v| * |u| * cos(θ)
Given that v * u = 12, |v| = 2, and |u| = 6√2, we can substitute these values into the formula and solve for θ:
12 = (2) * (6√2) * cos(θ)
Simplifying:
12 = 12√2 * cos(θ)
Dividing both sides by 12√2:
1 = cos(θ)
To find the value of θ, we need to take the inverse cosine (also known as arccos) of both sides:
θ = arccos(1)
The arccos of 1 is 0, so the value of θ is 0 degrees.