A) \[\frac{1}{\sqrt{14}},\,\,\frac{-3}{\sqrt{14}},\,\,\frac{2}{\sqrt{14}}\]
B) \[\frac{1}{\sqrt{14}},\,\,\frac{2}{\sqrt{14}},\,\,\frac{3}{\sqrt{14}}\]
C) \[\frac{-1}{\sqrt{14}},\,\,\frac{3}{\sqrt{14}},\,\frac{-2}{\sqrt{14}}\]
D) \[\frac{-1}{\sqrt{14}},\,\,\frac{-2}{\sqrt{14}},\,\,\frac{-3}{\sqrt{14}}\]
Correct Answer: A
Solution :
Key Idea: If \[a,\,\,\,b\] and \[c\] are the direction ratios of a line, then the direction cosines of a line are \[l=\frac{a}{\sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}},\,\,m=\frac{b}{\sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}}\] \[n=\frac{c}{\sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}}\] Given direction ratios are \[1,\,\,-3\] and \[2\]. \[\therefore \]Direction cosines are \[l=\frac{1}{\sqrt{{{1}^{2}}+{{(-3)}^{2}}+{{2}^{2}}}},\,\,m=-\frac{3}{\sqrt{{{1}^{2}}+{{(-3)}^{2}}+{{2}^{2}}}}\] \[n=\frac{2}{\sqrt{{{1}^{2}}+{{(-3)}^{2}}+{{(2)}^{2}}}}\] \[i.e.,\] \[l=\frac{1}{\sqrt{14}},\,\,m=-\frac{3}{\sqrt{14}},\,\,n=\frac{2}{\sqrt{14}}\] Note: In any line has only one direction cosine but the direction ratios may be more than one.
You need to login to perform this action.
You will be redirected in
3 sec
