If the plane `x/2+y/3+z/6=1` cuts the axes of coordinates at points, `A ,B ," and "C` , then find the area of the triangle `A B C`

Options

A. 18 sq unit
B. 36 sq unit
C. `3sqrt14" sq unit"`
D. `2sqrt14" sq unit"`

Answer

c

Explanation

Plane meets axes at `A(2, 0, 0), B(0, 3, 0) and C(0, 0, 6)`.
Then area of `DeltaABC` is
`" "(1)/(2) |vec(AB)xxvec(AC)|`
`" "(1)/(2)|(-2hati+3hatj)xx(-2hati+6hatj)|`
`" "=3sqrt(14)` sq units