A) 1
B) 2
C) 3
D) 4
Correct Answer: D
Solution :
\[\cos \theta =\frac{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}+{{c}_{1}}{{c}_{2}}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}}\sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}\] \[\frac{1}{\sqrt{2}}=\frac{2a-3+10}{\sqrt{{{1}^{2}}+{{2}^{2}}+{{1}^{2}}}\,\sqrt{{{a}^{2}}+{{3}^{2}}+{{5}^{2}}}}\] \[\Rightarrow \,\,9\,({{a}^{2}}+34)=2\,{{[2a+7]}^{2}}=\,2\,[4{{a}^{2}}+28a+49]\] \[\Rightarrow \,\,{{a}^{2}}-56a+208=0\,\,\Rightarrow \,\,a=4\].
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