Question

Which expression gives the vector joining \[P_1(x_1,y_1,z_1)\] to \[P_2(x_2,y_2,z_2)\]?

Options

• \[\vec{P_1P_2}=(x_1-x_2)\hat{i}+(y_1-y_2)\hat{j}+(z_1-z_2)\hat{k}\]

• \[\vec{P_1P_2}=(x_1+x_2)\hat{i}+(y_1+y_2)\hat{j}+(z_1+z_2)\hat{k}\]

• \[\vec{P_1P_2}=(x_2-x_1)\hat{i}+(y_2-y_1)\hat{j}+(z_2-z_1)\hat{k}\]

• \[\vec{P_1P_2}=(x_2x_1)\hat{i}+(y_2y_1)\hat{j}+(z_2z_1)\hat{k}\]

Answer 1

Each coordinate of the initial point is subtracted from the corresponding coordinate of the terminal point. Thus the components are \[x_2-x_1\], \[y_2-y_1\], and \[z_2-z_1\].