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
la=mb=nc=1
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B
la=mb=nc=2
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C
la=mb=nc=K, where K is any constant real number.
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D
None of these
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Solution

## The correct option is D la=mb=nc=K, where ‘K′ 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, la=mb=nc=K Value of `K' need not to be only 1 & 2, it can take any real value. Thus the other two options are incorrect.

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