A) \[2{{p}^{2}}\]
B) \[\frac{{{p}^{2}}}{2}\]
C) \[{{p}^{2}}\]
D) None of these
Correct Answer: C
Solution :
We have \[\overrightarrow{AB}\,.\,\overrightarrow{AC}+\overrightarrow{BC}\,.\,\overrightarrow{BA}+\overrightarrow{CA}\,.\,\overrightarrow{CB}\] \[(AB)\,(AC)\cos \theta +(BC)\,(BA)\cos ({{90}^{o}}-\theta )+0\] =\[AB(AC\cos \theta +BC\sin \theta )=AB\left( \frac{{{(AC)}^{2}}}{AB}+\frac{{{(BC)}^{2}}}{AB} \right)\] \[=A{{C}^{2}}+B{{C}^{2}}=A{{B}^{2}}={{p}^{2}}\].You need to login to perform this action.
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