Given that a 2 b 4 and the angle between a and b is pi6 fi

Given that |a| = 2, |b| = 4 and the angle between a and b is pi/6, find the following numbers. Please fill your final answers in the boxes and use the remaining space below to show your work.

Solution

a.b = |a||b| cos theta
So, a.b = 2*4*sqrt 3/2
a.b = 4 sqrt 3

proj ab| = a.b/|b|
Projection ab = 4(sqrt 3)/4 = Sqrt 3

|a*b| = |a||b| sin theta
a*b = 2*4*1/2
= 4