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The position vectors of the points A, B,...

The position vectors of the points A, B, C are `2 hati + hatj - hatk , 3 hati - 2 hatj + hatk and hati + 4hatj - 3 hatk ` respectively . These points

A

form an isosceles triangle

B

form a right angled triangle

C

are collinear

D

form a scalene triangle

Text Solution

Verified by Experts

The correct Answer is:
C
`AB=(3-2)hati+(-2-1)hatj+(1+1)hatk`
`=hati-3hatj+2hatk`
`BC=(1-3)hati+(4+2)hatj+(-3-1)hatk`
`=-2hati+6hatj-4hatk`
`CA=(2-1)hati+(1-4)hatj+(-1+3)hatk`
`=hati-3hatj-2hatk`
`|AB|=sqrt(1+9+4)=sqrt(24)`
`|BC|=sqrt(4+36+16)=sqrt(56)=2sqrt(14)`
`|CA|=sqrt(1+9+4)=sqrt(24)`
So, `|AB|+|AC|=|BC|` and angle between AB and BC is `180^(@)` so, points A,B and C cannot form an isosceles triangle.
Hence, A,B and C are collinear.
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