A) \[{{45}^{o}}\]
B) \[{{90}^{o}}\]
C) \[{{15}^{o}}\]
D) \[{{30}^{o}}\]
Correct Answer: B
Solution :
Here we have \[|\overrightarrow{a}|=\sqrt{1+1+{{(4)}^{2}}}=\sqrt{1+1+16}=\sqrt{18}=3\sqrt{2}\] \[|\overrightarrow{b}|=\sqrt{1+{{(-1)}^{2}}+{{(4)}^{2}}}=\sqrt{1+1+16}\] \[=\sqrt{18}=3\sqrt{2}\] Now \[|\overrightarrow{a}|=|\overrightarrow{b}|\] Now \[(\overrightarrow{a}+\overrightarrow{b})\,.\,(\overrightarrow{a}-\overrightarrow{b})=\,|\overrightarrow{a}{{|}^{2}}-|\overrightarrow{b}{{|}^{2}}\] \[=0\,\,\left[ |\overrightarrow{a}|\,\,=\,\,|\overrightarrow{b}| \right]\]
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