A) \[\left\langle \frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}} \right\rangle \]
B) \[\left\langle -\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}} \right\rangle \]
C) \[\left\langle -\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}} \right\rangle \]
D) \[\left\langle \frac{1}{3},\frac{1}{3},\frac{1}{3} \right\rangle \]
Correct Answer: A
Solution :
[a] Let\[\ell \], m, n are the dc?s of a line that is inclined equally at \[\alpha \]to the +ve direction of axes. Now, \[\ell =\cos \alpha ,m=\cos \alpha .n=\cos \alpha .\] Also, \[{{\ell }^{2}}+{{m}^{2}}+{{n}^{2}}=1\] \[3{{\cos }^{2}}\alpha =1.\] \[\cos \alpha =\frac{1}{\sqrt{3}}\] \[\therefore \] dc?s of the line are: \[\left\langle \frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}} \right\rangle \]
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