Question

Find Solution Asap BRANLIEST ​

Answer 1

$\langle- 7,3\rangle\langle 9,7\rangle=\langle-42\rangle$

Solution:

Given expression is $\langle- 7,3\rangle \cdot\langle 9,7\rangle$.

This is a vector dot product.

Let us first know the definition of vector dot product.

Definition of dot product:

The two vectors are $\mathrm{u}=\left(u_{1}, u_{2}\right)$ and $\mathrm{v}=\left(v_{1}, v_{2}\right)$.

The dot product of $\mathrm{u}=\left(u_{1}, u_{2}\right)$ and $\mathrm{v}=\left(v_{1}, v_{2}\right)$ is $\mathrm{uv}=\left\langle u_{1} v_{1}, u_{2} v_{2}\right\rangle$.

Here, $u_{1}=-9, v_{1}=3, u_{2}=9, v_{2}=7$

$\langle- 7,3\rangle\langle 9,7\rangle=\langle(-7)(9)+(3)(7)\rangle$

                   $=\langle- 63+21\rangle$

                   $=\langle- 42\rangle$

$\langle- 7,3\rangle\langle 9,7\rangle=\langle-42\rangle$

Hence the answer is $\langle- 7,3\rangle\langle 9,7\rangle=\langle-42\rangle.$