Question

If \[\vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}\] and \[\vec{b}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k}\], what is \[\vec{a}-\vec{b}\]?

Options

• \[(a_1b_1)\hat{i}+(a_2b_2)\hat{j}+(a_3b_3)\hat{k}\]

• \[(a_1+b_1)\hat{i}+(a_2+b_2)\hat{j}+(a_3+b_3)\hat{k}\]

• \[(a_1-b_1)\hat{i}+(a_2-b_2)\hat{j}+(a_3-b_3)\hat{k}\]

• \[(b_1-a_1)\hat{i}+(b_2-a_2)\hat{j}+(b_3-a_3)\hat{k}\]

Answer 1

Vector subtraction is performed by subtracting each corresponding component of \[\vec{b}\] from \[\vec{a}\]. This gives the stated \[\hat{i}\], \[\hat{j}\], and \[\hat{k}\] components.