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) none of these
Correct Answer: B
Solution :
Vector \[\vec{A}=3\vec{i}-4\vec{j}+5\vec{k},\]the direction Cosines of \[\vec{A}=\frac{3}{\sqrt{{{3}^{2}}+{{4}^{2}}+{{5}^{2}}}},\]\[\frac{-4}{\sqrt{{{3}^{2}}+{{4}^{2}}+{{5}^{2}}}},\] \[\frac{5}{\sqrt{{{3}^{2}}+{{4}^{2}}+{{5}^{2}}}}\] \[=\frac{3}{5\sqrt{2}},\frac{-4}{5\sqrt{2}},\frac{1}{\sqrt{2}}\]
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