A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{2}\]
C) \[{{\sin }^{-1}}\left( \frac{1}{\sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}} \right)\]
D) \[{{\cos }^{-1}}\left( \frac{pqr}{\sqrt{{{p}^{2}}+{{q}^{2}}r}} \right)\]
Correct Answer: B
Solution :
\[{{\vec{v}}_{1}}=(\log {{a}^{2}})\,\hat{i}+(\log {{b}^{2}})\hat{j}+(\log {{c}^{2}})\hat{k}\] \[{{\vec{v}}_{2}}=(q-r)\hat{i}+(r+p)\hat{j}+(p-q)\hat{k}\] \[{{\vec{v}}_{1}}\cdot {{\vec{v}}_{2}}=({{\log }^{2}})(q-r)+(\log {{b}^{2}})(r-p)+(\log {{c}^{2}})(p-q)\] \[\Rightarrow a=A{{R}^{p-1}},\,b=A{{R}^{q-1}},c=A{{R}^{r-1}}\] \[\therefore {{v}_{1}}\cdot {{v}_{2}}=\log ({{a}^{2(q-r)}}\cdot {{b}^{2(r-p)}}\cdot {{c}^{2(p-q)}}=0\]You need to login to perform this action.
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