wiz-icon
MyQuestionIcon
MyQuestionIcon
2
You visited us 2 times! Enjoying our articles? Unlock Full Access!
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

Open in App
Solution


From the figure,
OP2=x12+y12
OQ2=x22+y22
PQ2=x2-x12+y2-y12
Using cosine formula in OPQ, we get:
PQ2=OP2+OQ2-2OP·OQcosα
x2-x12+y2-y12=x12+y12+x22+y22-2OP·OQcosα
x22+x12-2x1x2+y22+y12-2y1y2=x12+y12+x22+y22-2OP·OQcosα
-2x1x2-2y1y2=-2OP·OQcosα
OP·OQcosα=x1x2+y1y2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
All About Lines
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon