Question

Find the position vector of the midpoint of the vector joining the points P(2,3,4) and Q(4,1,−2).

Answer 1

The position vector of the midpoint M of the vector joining points P(2,3,4) and Q(4,1,-2) is <3, 2, 1>.

Step-by-step explanation:

To find the position vector of the midpoint of the vector joining the points P(2,3,4) and Q(4,1,−2), you need to calculate the average of the x, y, and z coordinates of the points P and Q. The midpoint M can be found by taking the average of the corresponding coordinates of P and Q:

• Mx = (Px + Qx) / 2 = (2 + 4) / 2
• My = (Py + Qy) / 2 = (3 + 1) / 2
• Mz = (Pz + Qz) / 2 = (4 + (−2)) / 2

Therefore, the midpoint M's coordinates would be:

M = (3, 2, 1)

The position vector of the midpoint M would be represented as <3, 2, 1> in vector form.