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If the plane x/2+y/3+z/6=1 cuts the axes...

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`

A

18 sq unit

B

36 sq unit

C

`3sqrt14" sq unit"`

D

`2sqrt14" sq unit"`

Text Solution

Verified by Experts

The correct Answer is:
c
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
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