Question

For \[\vec{a}=(a_1,a_2,a_3)\] and \[\vec{b}=(b_1,b_2,b_3)\], which expression gives \[\vec{a}\cdot\vec{b}\]?

Options

• \[a_1^2+b_1^2+a_2^2+b_2^2+a_3^2+b_3^2\]

• \[a_1b_1+a_2b_2+a_3b_3\]

• \[a_1b_2+a_2b_3+a_3b_1\]

• \[a_1+b_1+a_2+b_2+a_3+b_3\]

Answer 1

The component form of the dot product is the sum of products of corresponding components.
Thus, \[\vec{a}\cdot\vec{b}=a_1b_1+a_2b_2+a_3b_3\].