Question

Which expansion is obtained from \[(\vec{a}+\vec{b})\cdot(\vec{a}+\vec{b})\]?

Options

• \[\vec{a}\cdot\vec{a}+\vec{a}\cdot\vec{b}+\vec{b}\cdot\vec{a}+\vec{b}\cdot\vec{b}\]

• \[\vec{a}\cdot\vec{a}+\vec{b}\cdot\vec{b}\]

• \[\vec{a}\cdot\vec{b}+\vec{b}\cdot\vec{a}\]

• \[\vec{a}\cdot\vec{a}+2\vec{a}\cdot\vec{b}-\vec{b}\cdot\vec{b}\]

Answer 1

Using the distributive property produces four dot-product terms.
The two middle terms are \[\vec{a}\cdot\vec{b}\] and \[\vec{b}\cdot\vec{a}\].