Find the area of triangle whose vertices are A(2,0)B(4,5)C(6,3)in vector method
To find the area of a triangle using vector methods, you can use the formula:
Area = 1/2 * | AB x AC |
Where AB represents the vector from point A to point B, AC represents the vector from point A to point C, and x represents the cross product of the two vectors.
Let's break down the steps to find the area of the triangle using vector method:
Step 1: Calculate the vectors AB and AC.
AB = B - A = (4, 5) - (2, 0) = (2, 5)
AC = C - A = (6, 3) - (2, 0) = (4, 3)
Step 2: Calculate the cross product of vectors AB and AC.
AB x AC = (2 * 3) - (5 * 4) = 6 - 20 = -14
Step 3: Find the absolute value of the cross product.
| AB x AC | = |-14| = 14
Step 4: Calculate the area of the triangle using the formula.
Area = 1/2 * | AB x AC | = 1/2 * 14 = 7
Therefore, the area of the triangle with vertices A(2,0), B(4,5), and C(6,3) using vector methods is 7 square units.