Question

Find the angle between the given vectors round your answer to the nearest tenth of a degree

U= (4, -6) V= (-6, -4)

Answer 1

We can use the dot product formula to find the angle between two vectors:

cos(theta) = (U dot V) / (|U| * |V|)

where U dot V is the dot product of U and V, and |U| and |V| are the magnitudes of U and V, respectively.

First, let's calculate U dot V:

U dot V = (4 * -6) + (-6 * -4) = -24 - (-24) = 0

Next, let's calculate the magnitudes of U and V:

|U| = sqrt(4^2 + (-6)^2) = sqrt(52)

|V| = sqrt((-6)^2 + (-4)^2) = sqrt(52)

Now we can substitute these values into the formula for cos(theta):

cos(theta) = 0 / (sqrt(52) * sqrt(52)) = 0

Since cos(theta) = 0, this means that the angle between U and V is 90 degrees or π/2 radians.