Position Vectors and Coordinate Geometry

Question

A space shuttle is moving in a straight line and is traveling at a constant speed. It takes 3 hours to get from A to B and 1 hour to get from B to C. Relative to a suitable set of axes, A is the point (4, -1, 7) and B is the point (16, -10, 10). Find the coordinates of C. Can u please show me the steps?

Answer 1

In the i,j,k unit vector coordinate system,

 

A = 4i - j + 7k

 

B = 16i - 10j + 10k

 

t₁ = 3 hrs

 

t₂ = 1 hr

 

Velocity going from A to B is

 

v = (B - A) / t₁ = (B - A) / 3 = [(16-4)i + (-10+1)j + (10-7)k] / 3 = 4i + -3j + k

 

C = B + vt₂ = B + v(1) = (16+4)i + (-10-3)j + (10+1)k = 20i - 13j + 11k

 

C = (20, -13, 11)