Question

Given three points in the Cartesian coordinate system as A (3,-2,1), B (-3,-3,5), and C(2,6,-4). Find the vector from A to the midpoint of the straight line joining B to C.

Answer 1

To find the vector from point A to the midpoint of the line joining points B and C, we need to find the midpoint first. The midpoint is the average of the x-coordinates, y-coordinates, and z-coordinates of B and C. Then, we can calculate the vector from A to M by subtracting the coordinates of A from the coordinates of M.

Step-by-step explanation:

To find the vector from point A to the midpoint of the line joining points B and C, we need to find the midpoint first. The midpoint is the average of the x-coordinates, y-coordinates, and z-coordinates of B and C. So, the midpoint M is ((-3+2)/2, (-3+6)/2, (5-4)/2) = (-0.5, 1.5, 0.5). Now, we can calculate the vector from A to M by subtracting the coordinates of A from the coordinates of M. The vector from A to M is (-0.5-3, 1.5-(-2), 0.5-1) = (-3.5, 3.5, -0.5).