If a plane cuts off intercepts `OA = a, OB = b, OC = c` from the coordinate axes 9where `'O'` is the origin). then the area of the triangle `ABC` is equal to

Options

A. `(1)/(2)(ab+bc+ac)`
B. `(1)/(2)abc`
C. `(1)/(2)(a^(2)b^(2)+b^(2)c^(2)+c^(2)a^(2))^(1//2)`
D. `(1)/(2)(a+b+c)^(2)`

Answer

c

Explanation

Plane meets axes at A(a,0,0), B(0,b,0) and C(0,0,c), Then area of `DeltaABC`
`=(1)/(2)|vec(AB)xxvec(AC)|`
`=(1)/(2)|(-ahati+bhatj)xx(-ahati+chatk)|`
`=(1)/(2)sqrt(a^(2)b^(2)+b^(2)c^(2)+c^(2)a^(2))`