Question

The area of the triangle with vertices (1, 2, 0), (1, 0, 2) and (0, 3, 1) in sq. unit is ______.

Options

• `sqrt(5)`

• `sqrt(7)`

• `sqrt(6)`

• `sqrt(3)`

Answer 1

The area of the triangle with vertices (1, 2, 0), (1, 0, 2) and (0, 3, 1) in sq. unit is `underlinebb(sqrt(6))`.

Explanation:

If A = (1, 2, 0), B = (1, 0 ,2) and C = (0, 3, 1),

then `vec(AB) = - 2hatj + 2hatk`, `vec(AC) = -i + j + k`

and the area of triangle ABC is `1/2 |vec(AB) xx vec(AC)|` 

and `|vec(AB) xx vec(AC)| = |(hati, hatj, hatk),(0, -2, 2),(-1, 1, 1)| = -4hati - 2hatj - 2hatk`

`|vec(AB) xx vec(AC)|/2`

= `|-4i - 2j - 2k|/2`

= `sqrt(16 + 4 + 4)/2`

= `sqrt(24)/2`

= `(2sqrt(6))/2`

= `sqrt(6)` sq.units