If O is the origin and P (2, 3,4) and Q (1, -2, 1) be any two points show that OP OQ.

Question

Philoid · Accepted Answer

Given O(0, 0, 0), P(2, 3, 4) So, OP = 2i + 3j + 4k

Q(1, -2, 1), So, OQ = i – 2j + k

To prove that OPOQ we have,

OP.OQ = 0, i.e. the angle between the line segments is

So, the dot product i.e. |OP||OQ|cos = 0,cos = 0,

OP.OQ = 0

Thus, (2i + 3j + 4k).( i – 2j + k) = 2 – 6 + 4 = 0

Hence, proved.