Question

Which of the triplet can not represent direction cosine 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. $(\frac{4}{\sqrt{77}},\frac{5}{\sqrt{77}},\frac{6}{\sqrt{77}})$
• D. $(\frac{2}{\sqrt{25}},\frac{3}{\sqrt{25}},\frac{4}{\sqrt{25}})$

Answer 1

Answer: (D)

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

In general, the direction cosine of a line is defined as the cosine of the angles between the positive directed lines and the coordinate axes.

So the direction cosine of a line $(\frac{2}{\sqrt{2}5},\frac{3}{\sqrt{2}5},\frac{4}{\sqrt{2}5})$ cannot be represented in triplet form

Option D is right answer