Find the angle θ between u = and v =.

The angle between two vectors is:

CosФ = u - v / Magnitude (u) x magnitude (v)

Magnitude of u = SQRT (7^2 + - 2^2) = SQRT (49 + 4) = SQRT (53)

Magnitude of v = SQRT (-1^2 + 2^2) = SQRT (1 + 4) = SQRT (5)

u x v = (7 x - 1) + (-2 x 2) = - 7 + - 4 = - 11

cosФ = - 11 / sqrt (53) x sqrt (5)

cosФ = - 11sqrt265) / 265

Ф = cos^-1 (-11sqrt265) / 265)

Ф=132.51 degrees.

132.5°

Step-by-step explanation:

u•v = |u| |v| cos (theta)

(7*-1) + (-2*2) = sqrt (53) * sqrt (5) cos (theta)

-7-4 = sqrt (265) cos (theta)

cos (theta) = - 11/sqrt (265)

theta = 132.510447078