The points A(1,0,1),B(–1,2,3) and C(0,1,2) are
Non-collinear
Collinear
Non-coplanar
None of the above
Identify the nature of the given points
Given : A(1,0,1),B(–1,2,3) and C(0,1,2)
Magnitude of AB→
AB→=(-1-1)2+(2-0)2+(3-1)2⇒AB→=4+4+4⇒AB→=23
Magnitude of BC→
BC→=(0-1)2+(1-2)2+(2-3)2⇒BC→=1+1+1⇒BC→=3
Magnitude of AC→
AC→=(0-1)2+(1-0)2+(2-1)2⇒AC→=1+1+1⇒AC→=3
Since, AB→=BC→+AC→
⇒ 23=3+3
Therefore, the point C is the mid point of AB then the points are collinear.
Hence, option B is the correct answer.