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The point having position vectors 2hati+...

The point having position vectors `2hati+3hatj+4hatk,3hati+4hatj+2hatk and 4hati+2hatj+3hatk` are the vertices of

A

A. right angled triangle

B

B. isosceles triangle

C

C. equilateral triangle

D

D. collinear

Text Solution

Verified by Experts

The correct Answer is:
C
Here, `OA=2hati+3hatj+4hatk`
`OB=3hati+4hatj+2hatk`
and `OC=4hati+2hatj+3hatk`
So, `AB=hati+hatj-2hatk,BC=hati-2hatj+hatk,CA=2hati-hatj-hatk`
Clearly, `|AB|=|BC|=|CA|=sqrt(6)`
So, these poins are vertices of an equilateral triangle.
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