Let ABC be a triangle the position vectors of whose vertices are respectively `hati+2hatj+4hatk, -2hati+2hatj+hatk and 2hati+4hatj-3hatk`. Then the `/_\ABC` is (A) isosceles (B) equilateral (C) righat angled (D) none of these

Options

A. isosceles
B. equilateral
C. right angled
D. none of these

Answer

C

Explanation

`vec(BC) = vec(OC)-vec(OB) = 4hati+2hatj-4hatk`
`" "vec(AB) = -3hati-3hatk, vec(AC) = hati=2hatj- 7hatk`
`" "BC^(2) = 36, AB^(2) = 18, AC^(2)= 54 `
Cleary, `AC^(2) = BC^(2)m + AB^(2)`
`therefore angleB= 90^(@)`