t_n_p said:
malawi_glenn said:
The formula for finding the area of a triangle formed by vectors is A = 1/2 |a x b|, where a and b are the two vectors that form two sides of the triangle. |a x b| represents the magnitude of the cross product of the two vectors.
To find the vectors needed, you will need to know the coordinates of the three vertices of the triangle. Then, you can use the coordinates to create two vectors, one from the first vertex to the second vertex and another from the first vertex to the third vertex.
No, the area of a triangle formed by vectors cannot be negative. The magnitude of the cross product in the formula always results in a positive value, and when multiplied by 1/2, it will always result in a positive area.
Yes, it is necessary to use vectors to calculate the area of a triangle. The cross product of two vectors is used to determine the area of a parallelogram, and since a triangle is half of a parallelogram, the formula for the area of a triangle involves dividing the magnitude of the cross product by 2.
No, the area of a triangle formed by vectors cannot be greater than the sum of its side lengths. This is because the formula for the area of a triangle formed by vectors involves taking the magnitude of the cross product, which is always less than or equal to the product of the magnitudes of the two vectors.