The figure on the right shows vectors a b and c and a gray t

The figure on the right shows vectors a, b and c and a gray triangle. Use the duplicate figures below to sketch the vectors b - 2a and proj_a b. b - 2a: Express the vector c in terms of a and b: c = 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. a b = |proj_a b| = |a times b| = Area of the gray triangle =

Solution

for q1 image is not clear. Can you please rotate and then post.

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