Question

Can $\frac{1}{\sqrt{3}},\frac{2}{\sqrt{3}},\frac{-2}{\sqrt{3}}$ be the direction cosines of any directed line?

• A. Yes
• B. No
• C. Cannot say
• D. None of these

Answer 1

Answer: (B)

No

No, they can not be the direction cosines of any directed line.

As the sum of square of them is not $1$.

As ${\left(\frac{1}{\sqrt{3}}\right)}^2+$${\left(\frac{2}{\sqrt{3}}\right)}^2$$+{\left(\frac{-2}{\sqrt{3}}\right)}^2$

$=\frac{1+4+4}{3}$

$=3$.