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Let vec a , vec b and vec c be unit vec...

Let ` vec a , vec b` and `vec c` be unit vectors such that ` vec a+ vec b- vec c=0.` If the area of triangle formed by vectors ` vec a and vec b` is `A ,` then what is the value of `4A^2?`

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The correct Answer is:
3
Given a+b=c
Now, vector c is along the diagonal of the parallelogram which has adjacent side vectors a and b. sincne, c is also a unit vector, triangle formed by vectors a and b is an equilateral triangle.
Then, area of triangle `=(sqrt(3))/(4)impliesA^(2)=(3)/(10)implies16A^(2)=3`.
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