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Question

If the position vectors of the points A, B, and C be i+j , i−j and ai+bj+ck respective;y , then the points A, B and C are collinear if:

A
a=b=c=1
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B
a=1 , b and c are arbitrary scalars
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C
a=b=c=0
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D
c=0 , a=1 and b is a arbitrary scalar.
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Solution

The correct option is C c=0 , a=1 and b is a arbitrary scalar.
Given points are A(i+j) , B(ij) and C(ai+bj+ck)

These three points are collinear if drs of lines AB and CB are proportional

We have AB=2j and CB=(a1)i+(b+1)j+ck

Since their drs are proportional, we get a10=b+12=c0

c=0,a=1 and b can be a arbitrary scalar
Therefore option D is correct

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