vectors and angles

Here are some two dimensional vectors. Find the difference between the vectors, both U-V and V-U, the dot products U·U, V·V, U·V, length of the vectors and the cosine of the angle between them, which is given by the formula in the picture above.

Example

U = <4 3> and V = <0 5>

U·U =  25

V·V =  25

U·V = 15

||U|| = sqrt(25) = 5

||V|| = sqrt(25) = 5

costheta = 15/25 = 3/5

theta ~= 53.1301°

Practice.

U = <4 3> and V = <3 -4>

U·U = ______

V·V =  ______

U·V =______

||U|| = ______

||V|| = ________

costheta = ______

theta = _______

U-V = _______

||U-V|| = _________

cosine of angle between U and U-V = ________


angle to nearest thousandth of a degree = _______


V-U = _______

||V-U|| = _________

cosine of angle between V and V-U = ________


angle to nearest thousandth of a degree = _______



Answers in the comments.