Answer:
The position vector of point C is <-3 , -17 , 8> or -3i - 17j + 8k
Step-by-step explanation:
* Lets revise how to solve the problem
- If the endpoints of a segment are (x1 , y1 , z1) and (x2 , y2 , z2), and
point (x , y , z) divides the segment externally at ratio m1 :m2, then
* Lets solve the problem
∵ AB is a segment where A = (3 , 1 , 2) and B = (1 , - 5 , 4)
∵ Point C lies on line AB such that AC : BC=3 : 2
∵ From the ratio AC = 3/2 AB
∴ C divides AB externally
- Lets use the rule above to find the coordinates of C
- Let Point A is (x1 , y1 , z1) , point B is (x2 , y2 , z2) and point C is (x , y , z)
and AC : AB is m1 : m2
∴ x1 = 3 , x2 = 1
∴ y1 = 1 , y2 = -5
∴ z1 = 2 , z2 = 4
∴ m1 = 3 , m2 = 2
- By using the rule above
∴
∴
∴
∴ The coordinates fo point c are (-3 , -17 , 8)
* The position vector of point C is <-3 , -17 , 8> or -3i - 17j + 8k