Which of the triplets cannot represent direction cosines of a lin… - Vidyadip

MCQ

Which of the triplets cannot represent direction cosines of a line?

A
$\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}$
B
$\frac{3}{\sqrt{50}}, \frac{4}{\sqrt{50}}, \frac{5}{\sqrt{50}}$
C
$\frac{4}{\sqrt{77}}, \frac{5}{\sqrt{77}}, \frac{6}{\sqrt{77}}$
✓
$\frac{2}{\sqrt{25}}, \frac{3}{\sqrt{25}}, \frac{4}{\sqrt{25}}$

✓

Answer

Correct option: D.

$\frac{2}{\sqrt{25}}, \frac{3}{\sqrt{25}}, \frac{4}{\sqrt{25}}$

(D) We know that, $l^2+ m ^2+ n ^2=1$
Consider option (D)
$\left(\frac{2}{\sqrt{25}}\right)^2+\left(\frac{3}{\sqrt{25}}\right)^2+\left(\frac{4}{\sqrt{25}}\right)^2=\frac{4+9+16}{25}$
$=\frac{29}{25} \neq 1$
$\therefore \quad$ correct answer is option (D).

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