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L:(x,y,z) = (t,t,t) and i need to find a triangle with the minimum area possible.

My initial approach was to calculate the vector BA and BC and then apply both vectors in the area triangle formula 1/2||BAxBC|| = area and then find a t that gives me the minimum area, but then im wondering if this is correct since there may be a possibility that t can be canceled out and i'm left with a constant that comes from the derivate of the cross product.