Question

if |x|=2 and |y|=5, determine the dot product between x-2y and x+3y if the angle between vector x and y is 60deg.

Answer 1

say X = 2 i + 0 j
Y = 5 cos 60 i + 5 sin 60 j
Y = 2.5 i + 4.33 j

then
X - 2Y = -3 i - 8.66 j
X + 3Y = etc, I think you can do it from there

Answer 2

x dot y = 2 x 5 x cos60 = 5

Use the distributive property:
(x-2y) dot (x+3y)
= x dot x - 2(x dot y) + 3 (x dot y) - 6(y dot y)
= x dot x + (x dot y) - 6(y dot y)
= |x|^2 + (x dot y) - 6|y|^2
= 4 + 5 - 150
=-141