A) \[{{90}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{30}^{o}}\]
D) \[{{15}^{o}}\]
Correct Answer: A
Solution :
\[\mathbf{a}=(1,\,1,\,4)=\mathbf{i}+\mathbf{j}+4\mathbf{k},\] \[\mathbf{b}=(1,\,-1,\,4)=\mathbf{i}-\mathbf{j}+4\mathbf{k}\] \ \[\mathbf{a}+\mathbf{b}=2\mathbf{i}+8\mathbf{k}\] Þ \[\mathbf{a}-\mathbf{b}=2\mathbf{j}\] Since, \[(\mathbf{a}+\mathbf{b})\,.\,(\mathbf{a}-\mathbf{b})=0\] \ \[(\mathbf{a}+\mathbf{b})\bot (\mathbf{a}-\mathbf{b})\]. Hence \[\theta =90{}^\circ \].
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