1.

If the position vectors of the vertices of Delta ABC are 3hati+hatj+2hatk, hati-2hatj+7hatk and -2hati+3hatj+5hatk, then the DeltaABC is

Answer»

right angled and isosceles
right angled, but not isosceles
isosceles but not right angled
equilateral

Solution :Given vertices are
`A(3hati+hatj+2hatk),B(hati-2hatj+7hatk)andC(-2hati+3hatj+5hatk)`.
Now, `AB=(hati-2hatj+7hatk)-(3hati+hatj+2hatk)`
`=-2hati-3hatj+5hatk`
`THEREFORE |AB|=sqrt(4+9+25)=sqrt(38)`
Similarly, `|BC|=|CA|=sqrt(38)`
`therefore |AB|=|BC|=|CA|=sqrt(38)`
HENCE, triangle is an equilateral triangle.


Discussion

No Comment Found

Related InterviewSolutions