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.
