Question

If the direction cosines of a line are $(-\frac{2}{\sqrt{21}},\frac{C}{\sqrt{21}},\frac{1}{\sqrt{21}})$ then the value of $C$ is

• A. $6$
• B. $4$
• C. $-4$
• D. $2$

Answer 1

Answer: (B), (C)

The correct options are
B $4$
C $-4$

Given that the directional cosines of a line is $-\frac{2}{\sqrt{21}},\frac{C}{\sqrt{21}},\frac{1}{\sqrt{21}}$

We know that the sum of squares of directional cosines is equal to $1$

$\Rightarrow {(-\frac{2}{\sqrt{21}})}^2+{\left(\frac{C}{\sqrt{21}}\right)}^2+{\left(\frac{1}{\sqrt{21}}\right)}^2=1$

$\Rightarrow C^2=21-4-1=16$

$\Rightarrow C=\pm 4$

So the correct option is $B,C$