Hi I am having trouble with this linear algebra question bel

Hi I am having trouble with this linear algebra question below. I dont know where to start, thanks!

Consider the points A = (2,6, -9) B = (-2, 10, -2) C = (2, 2, -6) and the vector d = 3i + 2j + 7k. Find AB. BC and AC. Find ||AB|| and ||OA||. Calculate the exact distance from point B to point C. Find a unit vector in the direction AC. Find the coordinates of the midpoint of DC. Find the projection of d in the direction of AB i.e. d_||. and also find d. What is the angle between OB and d? What is the angle between BC and AC?

Solution

A = ( 2, 6 , -9) ; B = ( -2 , 10, -2) and C = ( 2 , 2 , -6)

a) AB = OB - OA = ( -2, 10, -2) - ( 2, 6, -9) = (-4 ,4,7)

BC = OC - OB = ( 2 , 2 , -6) - ( -2 , 10, -2) = ( 4, -8 , -4)

AC = OC - OA = ( 2 , 2 , -6) - ( 2, 6 , -9) = ( 0 , -4 , 3)

b) ||AB|| = sqrt( 4^2 +4^2 + 7^2) = sqrt(65)

||OA|| = sqrt( 2^2 +6^2 +9^2) = 11

c) Distance between B to C = || OC -OB|| = sqrt( 4^2 +8^2 +4^2) = sqrt(16 +16 +64)

= sqrt(96)

d) Unit vector in direction of AC = ( 0 , -4 , 3)/||AC|| = (0, -4 , 3) /sqrt25 = (0, -4/5 , 3/25)

e) Midpoint BC =  OC + ½BC = (2, 2, -6) + 1/2(4, -8 , -4) =

= (2, 2, -6) + (2, -4 , -2)

= ( 4 , -2, -8)