A) \( \Large a_{1}a_{2}+b_{1}b_{2} \) |
B) \( \Large a^{2}_{1}+a^{2}_{2}+b^{2}_{1}+b^{2}_{2} \) |
C) \( \Large a^{2}_{1}-a^{2}_{2}+b^{2}_{1}-b^{2}_{2} \) |
D) none of these |
A) \( \Large a_{1}a_{2}+b_{1}b_{2} \) |
We know, \( \Large \cos \theta = \frac{OP^{2}+OQ^{2}-PQ^{2}}{2OP.OQ} \)
=> \( \Large 2OP.OQ \cos \theta = a^{2}_{1}+b^{2}_{1}+a^{2}_{2}+b^{2}_{2} \) \( \Large - \left[ \left(a_{1}-a_{2}\right)^{2}+ \left(b_{1}-b_{2}\right)^{2} \right] \)
=> \( \Large OP.OQ \cos \theta = a_{1}a_{2}+b_{1}b_{2} \)