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Let veca,vecb,vecc be the position vecto...

Let `veca,vecb,vecc` be the position vectors of three vertices A,B,C of a triangle respectively. Then the area fo the triangle 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|`

Text Solution

Verified by Experts

The correct Answer is:
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|`
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