Question

If the line segment joining the points P(x₁, y₁) and Q(x₂, y₂) subtends an angle α at the origin O, prove that : OP. OQ cos α = x₁ x₂ + y₁ y₂.

Answer 1

Given,

Two points P and Q subtends an angle α at the origin as shown in figure:

From figure we can see that points O, P and Q forms a triangle.

Clearly in ΔOPQ we have:

Hence proved.