Question

Dot Product
Suppose that u and v are vectors in R to the seventh power both of length 2 the square root of 2 and that the length of u − v is also2 the square root of 2 . Then parallel to u plus v parallel-to = ____________ and the angle between u and v is _____________.

Answer 1

|u-v|² = |u|² + |v|² - 2*|u|*|v|*cos$\theta$

(2$\sqrt{2}$)² = (2$\sqrt{2}$)² + (2$\sqrt{2}$)² - 2*(2$\sqrt{2}$)*(2$\sqrt{2}$)*cos$\theta$

8 = 8 + 8 - 16*cos$\theta$

cos$\theta$=0.5

$\theta$ = $\pi$/3

Suppose that u and v are vectors in R to the seventh power both of length 2 the square root of 2 and that the length of u − v is also2 the square root of 2 . Then parallel to u plus v parallel-to = k*(u+v) (where k=const) and the angle between u and v is $\pi$/3 radian.