Which of the following can not be the directi | vedclass

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(C) The direction cosines $l, m, n$ of a line must satisfy the condition $l^2 + m^2 + n^2 = 1$. For option $A$: $(\sqrt{\frac{1}{5}})^2 + (-\sqrt{\fra

Vedclass · Accepted Answer

$\frac{1}{\sqrt{2}}, \frac{-1}{\sqrt{2}}, \frac{-1}{\sqrt{2}}$

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(C) The direction cosines $l, m, n$ of a line must satisfy the condition $l^2 + m^2 + n^2 = 1$. For option $A$: $(\sqrt{\frac{1}{5}})^2 + (-\sqrt{\frac{1}{2}})^2 + (\sqrt{\frac{3}{10}})^2 = \frac{1}{5} + \frac{1}{2} + \frac{3}{10} = \frac{2+5+3}{10} = \frac{10}{10} = 1$. For option $B$: $(\frac{1}{\sqrt{3}})^2 + (\frac{-1}{\sqrt{3}})^2 + (\frac{1}{\sqrt{3}})^2 = \frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 1$. For option $C$: $(\frac{1}{\sqrt{2}})^2 + (\frac{-1}{\sqrt{2}})^2 + (\frac{-1}{\sqrt{2}})^2 = \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = \frac{3}{2} 
eq 1$. For option $D$: $(\frac{1}{\sqrt{2}})^2 + (\frac{-1}{\sqrt{2}})^2 + 0^2 = \frac{1}{2} + \frac{1}{2} + 0 = 1$. Since the sum of squares for option $C$ is not $1$,it cannot be the direction cosines of a line.

Which of the following can not be the direction cosines of a line?

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