# Vector Proof (1)

Prove that:

$\left( \begin{matrix} { a }_{ 1 } \\ { a }_{ 2 } \\ { a }_{ 3 } \end{matrix} \right) \left( \begin{matrix} { b }_{ 1 } \\ { b }_{ 2 } \\ { b }_{ 3 } \end{matrix} \right) ={ a }_{ 1 }{ b }_{ 1 }+{ a }_{ 2 }{ b }_{ 2 }+{ a }_{ 3 }{ b }_{ 3 }\\ \\$

Firstly, look at the image below.

You should know that, if $\underline { a } \\ \\$ and $\underline { b } \\ \\$ are perpendicular $\underline { a } \cdot \underline { b } =0\\ \\$.

You should also know these rules:

$\left| \underline { i } \right| \left| \underline { i } \right| ={ \underline { i } }^{ 2 }=1\cdot 1=1\\ \\ \left| \underline { j } \right| \left| \underline { j } \right| ={ \underline { j } }^{ 2 }=1\cdot 1=1\\ \\ \left| \underline { k } \right| \left| \underline { k } \right| ={ \underline { k } }^{ 2 }=1\cdot 1=1\\ \\$

Knowing these rules, we can say that:

*Click on the proof above to see it in full.