Question

Which expression gives the magnitude of \[\vec{P_1P_2}\] for \[P_1(x_1,y_1,z_1)\] and \[P_2(x_2,y_2,z_2)\]?

Options

• \[|\vec{P_1P_2}|=(x_2-x_1)+(y_2-y_1)+(z_2-z_1)\]

• \[|\vec{P_1P_2}|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\]

• \[|\vec{P_1P_2}|=\sqrt{x_2^2-x_1^2+y_2^2-y_1^2+z_2^2-z_1^2}\]

• \[|\vec{P_1P_2}|=(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2\]

Answer 1

The magnitude is found by taking the square root of the sum of the squares of the three component differences. This magnitude equals the distance between the two points.