find angle between x-axis and A-B

Question

Where A=2i+2j-k and B=6i-3j+2k

Answer 1

 

Hi Hamza,

 

A - B = (2i+2j-k) - (6i-3j+2k)

= -4i+5j-3k

Consider a right triangle of which vertices are

O = (0,0,0), X = (-4,0,0), and Y = (-4,5,-3).

The angle between YO and XO is

     cos^-1('length of XO'/'length of YO')

             = cos^-1(4/√((-4)²+5²+(-3)²))

             = cos-1(4/√50)

             = 0.9695 rad

As this is the angle between A-B and the negative direction of the x-axis,

the angle between A-B and the positive direction of the x-axis is

π - 0.9695 = 2.1721 rad