Question

Which expression represents scalar multiplication of \[\vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}\] by \[\lambda\]?

Options

• \[\lambda\vec{a}=(\lambda a_1)\hat{i}+(\lambda a_2)\hat{j}+(\lambda a_3)\hat{k}\]

• \[\lambda\vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}+\lambda\]

• \[\lambda\vec{a}=\lambda(a_1+a_2+a_3)\]

• \[\lambda\vec{a}=(a_1+\lambda)\hat{i}+(a_2+\lambda)\hat{j}+(a_3+\lambda)\hat{k}\]

Answer 1

Scalar multiplication multiplies every component of the vector by the scalar \[\lambda\]. Therefore each coefficient of \[\hat{i}\], \[\hat{j}\], and \[\hat{k}\] is multiplied by \[\lambda\].