Question

The points A , B and C have the following position vectors with respect to an origin O.
OA= 2i + j -2k
OB= 2i - j + 2k
OC= i + 3j + 3k
Find the vector equation of the line (BC)

Answer 1

Given info : The points A , B and C have the following position vectors with respect to an origin O.

OA= 2i + j -2k

OB= 2i - j + 2k

OC= i + 3j + 3k

To find : the equation of line BC.

Solution : from triangle rule,

OB + BC = OC [ see figure ]

so, BC = OC - OB

⇒BC = (i + 3j + 3k) - (2i - j + 2k)

⇒BC = (1 - 2)i + (3 + 1)j + (3 - 2)k

⇒BC = -i + 4j + k

Therefore the equation of line BC is -i + 4j + k.