A) \[\frac{3}{5},\,\frac{-4}{5},\frac{1}{5}\]
B) \[\frac{3}{5\sqrt{2}},\,\frac{-4}{5\sqrt{2}},\frac{1}{\sqrt{2}}\]
C) \[\frac{3}{\sqrt{2}},\,\frac{-4}{\sqrt{2}},\,\frac{1}{\sqrt{2}}\]
D) \[\frac{3}{5\sqrt{2}},\,\,\frac{4}{5\sqrt{2}},\,\frac{1}{\sqrt{2}}\]
Correct Answer: B
Solution :
Vector \[\overrightarrow{A}=3i-4j+5k\]. We know that direction cosines of \[\overrightarrow{A}\]\[=\frac{3}{\sqrt{{{3}^{2}}+{{4}^{2}}+{{5}^{2}}}},\,\frac{-4}{\sqrt{{{3}^{2}}+{{4}^{2}}+{{5}^{2}}}},\,\frac{5}{\sqrt{{{3}^{2}}+{{4}^{2}}+{{5}^{2}}}}\] \[=\frac{3}{5\sqrt{2}},\,\frac{-4}{5\sqrt{2}},\,\frac{1}{\sqrt{2}}\].
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