Calculate if vw 3 and the angle between v and w is pi 6Sol

Calculate if v.w = 3, and the angle between v and w is pi / 6.

Solution

v dot w = |v||w|cos theta

3 = (2)|w|cos(pi/6)

3/(2 * cos(pi/6)) = |w|

3/sqrt(3) = |w|

sqrt(3) = |w|

|w| = sqrt(3)

|v cross w| = |v||w|sin theta

|v cross w| = 2 sqrt(3) sin(pi/6)

|v cross w| = sqrt(3)