Find the area of the triangle formed by the points A(1, 2, 3), B(4, 5, 6), and C

Find the area of the triangle formed by the points A(1, 2, 3), B(4, 5, 6), and C(7, 8, 9). (2022)

Find the area of the triangle formed by the points A(1, 2, 3), B(4, 5, 6), and C(7, 8, 9). (2022)

Step 1: Understand that a triangle is formed by three points in space.
Step 2: Identify the given points: A(1, 2, 3), B(4, 5, 6), and C(7, 8, 9).
Step 3: Check if the points are collinear (on the same straight line).
Step 4: To check for collinearity, calculate the vectors AB and AC.
Step 5: Find vector AB by subtracting the coordinates of A from B: AB = B - A = (4-1, 5-2, 6-3) = (3, 3, 3).
Step 6: Find vector AC by subtracting the coordinates of A from C: AC = C - A = (7-1, 8-2, 9-3) = (6, 6, 6).
Step 7: Check if vectors AB and AC are scalar multiples of each other.
Step 8: Notice that AC = 2 * AB, which means they are collinear.
Step 9: Since the points are collinear, the area of the triangle formed by these points is 0.

Collinearity of Points – The concept of determining whether three points in space are collinear, which means they lie on the same straight line.
Area of a Triangle – The formula for calculating the area of a triangle formed by three points in a coordinate system, which is zero if the points are collinear.