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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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