Question

If ` veca , vecb, vecc` are the position vectors of the vertices. A,B,C of a triangle ABC. Then the area of triangle ABC is
A. ` 1/2 |veca xx vecb +vecb xx vecc +vecc xx veca|`
B. `1/2|veca xx vecb|`
C. ` 1/2|vecb xx vecc|`
D. ` 1/2 |vecc xx veca|`

Answer 1

Correct Answer - A
we have,
Area of ` triangleABC = 1/2|vec(AB) xx vec(AC)|`
Now, ` vec(AB) xx vec(AC) = (vecb -veca) xx (vecc -veca)`
` Rightarrow vec(AB) xx vec(AC) = vecb xx vecc -vecb xx veca -veca xx vecc +veca xx veca`
` Rightarrow vec(AB) xx vec(AC) = vecb xx vecc + veca xx vecb +vecc xx veca +vec0`
` Rightarrow vec(AB) xx vec(AC) =veca xx vecb +vecb xx vecc + vecc xx veca`
Area of `Triangle ABC = 1/2 |vec(AB) xx vec(AC)|`
` Rightarrow " Area of " triangle ABC = 1/2 |veca xx vecb +vecb xx vecc + vecc xx veca|`