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Which of the following represents direction cosines of the line?
Question

Which of the following represents direction cosines of the line?

A.

0,12,120,\frac{1}{2},\frac{1}{2}​​

B.

0,32,120,\frac{\sqrt3}{2},\frac{1}{2}​​

C.

13,13,13\frac{1}{3},\frac{1}{3},\frac{1}{3}​​

D.

0,13,130,\frac{1}{\sqrt3},\frac{1}{3}​​

Correct option is B

Direction cosines l,m,n of a line must satisfy the condition:l2+m2+n2=1So, for each option, we compute:l2+m2+n2Only the one that gives 1 will be the valid set of direction cosines.Option B:l=0,m=32,n=1202+(32)2+(12)2=34+14=44=1\begin{aligned}&\text{Direction cosines } l, m, n \text{ of a line must satisfy the condition:} \\&\quad l^2 + m^2 + n^2 = 1 \\\\&\text{So, for each option, we compute:} \\&\quad l^2 + m^2 + n^2 \\&\text{Only the one that gives 1 will be the valid set of direction cosines.} \\\\&\text{\underline{Option B:}} \\&\quad l = 0, \quad m = \frac{\sqrt3}{2}, \quad n = \frac{1}{2} \\&\quad 0^2 + \left( \frac{\sqrt3}{2} \right)^2 + \left( \frac{1}{2} \right)^2 = \frac{3}{4} + \frac{1}{4} = \frac{4}{4} = 1 \\\end{aligned}​​

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