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If the position vectors of the points A,...

If the position vectors of the points A,B and C be `hati+hatj,hati-hatj` and `ahati+bhatj+chatk` respectively, then the points A,B and C are collinear, if

A

a=b=c=1

B

a=1,b and c are arbitrary scalars

C

ab=c=0

D

c=0,a=1 and b is arbitrary scalars

Text Solution

Verified by Experts

The correct Answer is:
D
Here, `AB=-2hatj,BC=(a-1)hati+(b+1)hatj+chatk`
The points are collinear, then `AB=k(BC)`
`-2hatj=k{(a-1)hati+(b+1)hatj+chatk}`
On comparing, `k(a-1)=0,k(b+1)=-2,kc=0`
Hence, c=0,a=1 and b is arbitrary scalar.
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