The direction cosines of a line are l, m and n, and the direction ratios of the same line are a, b & c. Then, the expression is always correct.

l a + m b + n c = 1

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\frac{l}{a} = \frac{m}{b} = \frac{n}{c} = k

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\frac{l}{a} = \frac{m}{b} = \frac{n}{c} = 1

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Solution

The correct option is B $\frac{l}{a} = \frac{m}{b} = \frac{n}{c} = k$
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 non-zero real number.
Or, $\frac{l}{a} = \frac{m}{b} = \frac{n}{c} = K$

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The direction cosines of a line are l, m and n, and the direction ratios of the same line are a, b & c. Then, the expression is always correct.

The correct option is B la=mb=nc=kWe 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 non-zero real number. Or, la=mb=nc=K