A nonzero vector is a vector that has a magnitude (length) and direction, and is not equal to the zero vector (a vector with a magnitude of 0).
To find the nonzero vector of a triangle, you can use the cross product or vector product of two of its sides. This will give you a vector that is perpendicular to both sides and has a magnitude equal to the area of the triangle.
The formula for finding the area of a triangle is A = 1/2 * b * h, where b is the base of the triangle and h is the height. Alternatively, you can also use Heron's formula, which takes into account all three sides of the triangle: A = √(s(s-a)(s-b)(s-c)), where s is the semiperimeter (half of the perimeter) and a, b, and c are the lengths of the sides.
To find the area of a triangle using vectors, you can use the magnitude of the cross product or vector product of two of its sides. This will give you the area of the parallelogram formed by those two sides, and since a triangle is half of a parallelogram, you can divide the result by 2 to get the area of the triangle.
Yes, it is possible for the nonzero vector and area of a triangle to be negative. This would occur if the orientation of the triangle is reversed or if the angle between the two sides used to find the vector or area is greater than 180 degrees.