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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.
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.
Brief review of Cartesian System of Rectangular Coordinates | CBSE | Class 11 | Exercise 22.1 | Maths | RD Sharma
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.

Solution:

According to the question, two points P and Q make an angle α at the origin. This is shown in the figure:

It can be observed from the figure that points P, O and Q form a triangle. So, in ΔOPQ by using cosine formula we have:

\[\cos \alpha =\frac{O{{P}^{2}}+O{{Q}^{2}}-P{{Q}^{2}}}{2OP.OQ}\]

i

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