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Question

# If 1,2,1 are the direction ratios of a line then which of the following could be direction cosines of this line?

A
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B
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C
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D
None of these
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Solution

## The correct option is B We know that the direction ratios are proportional to direction cosines. I.e. l = k.a, m = k.b , n = k.c where k is any constant, l,m & n are direction cosines and a,b & c are direction ratios. We also know that l2+m2+n2=1 So,(K.a)2+(K.b)2+(K.c)2=1 K2(a2+b2+c2)=1 k2=1(a2+b2+c2) Or, K=±√1(a2+b2+c2) In the question given direction ratios or a,b,c are 1, 2, 1. So, K=±√1((1)2+(2)2+(1)2) Or, K=±√16 So the direction cosines will be - I=1.k or,l=√16(on taking k as √16) Similarly ,m=2.√16 & n=√16 Also,-√16,−2.√16,−√16 on taking k as −√16

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