[tex]\langle- 7,3\rangle\langle 9,7\rangle=\langle-42\rangle[/tex]
Solution:
Given expression is [tex]\langle- 7,3\rangle \cdot\langle 9,7\rangle[/tex].
This is a vector dot product.
Let us first know the definition of vector dot product.
Definition of dot product:
The two vectors are [tex]\mathrm{u}=\left(u_{1}, u_{2}\right)[/tex] and [tex]\mathrm{v}=\left(v_{1}, v_{2}\right)[/tex].
The dot product of [tex]\mathrm{u}=\left(u_{1}, u_{2}\right)[/tex] and [tex]\mathrm{v}=\left(v_{1}, v_{2}\right)[/tex] is [tex]\mathrm{uv}=\left\langle u_{1} v_{1}, u_{2} v_{2}\right\rangle[/tex].
Here, [tex]u_{1}=-9, v_{1}=3, u_{2}=9, v_{2}=7[/tex]
[tex]\langle- 7,3\rangle\langle 9,7\rangle=\langle(-7)(9)+(3)(7)\rangle[/tex]
[tex]=\langle- 63+21\rangle[/tex]
[tex]=\langle- 42\rangle[/tex]
[tex]\langle- 7,3\rangle\langle 9,7\rangle=\langle-42\rangle[/tex]
Hence the answer is [tex]\langle- 7,3\rangle\langle 9,7\rangle=\langle-42\rangle.[/tex]
