Question

If the direction cosines of a line are l, m and n and the direction ratios of the same line are a, b & c then which of the following is always correct ?

• A. $\frac{l}{a}=\frac{m}{b}=\frac{n}{c}=1$
• B. $\frac{l}{a}=\frac{m}{b}=\frac{n}{c}=2$
• C. $\frac{l}{a}=\frac{m}{b}=\frac{n}{c}=K$, where $‘K^{\prime }$ is any constant real number.
• D. None of these

Answer 1

Answer: (C)

$\frac{l}{a}=\frac{m}{b}=\frac{n}{c}=K$, where $‘K^{\prime }$ is any constant real number.

We have seen that directions ratios of any line segment would be proportional to the direction cosines. i.e. $l=K.a,m=K.b,n=K.c$ ; where $K$ is any constant real number.
or, $\frac{l}{a}=\frac{m}{b}=\frac{n}{c}=K$
Value of `$K$' need not to be only 1 & 2, it can take any real value. Thus the other two options are incorrect.