If the position vectors of the vertices A,B and C of a `DeltaABC` are `7hatj+10k,-hati+6hatj+6hatk and -4hati+9hatj+6hatk`, respectively, the triangle is

Options

A. equilateral
B. isosceles
C. scalene
D. right angled and isosceles also

Answer

D

Explanation

Given position vectors of A,B and C are `7hatj+10hatk,-hati+6hatj+6hatk and -4hati+9hatj+6hatk`, respectively.
`therefore|AB|=|-hati-hatj-4hatk|=sqrt(18)`
`|BC|=|-3hati+3hatj|=sqrt(18)`
`|AC|=|-4hati+2hatj-4hatk|=sqrt(36)`
Clearly, `AB=BC and (AC)^(2)=(AB)^(2)+(BC)^(2)`
Hence, triangle is right angled isosceles.