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Question

The vectors $\mathbf { u }$ and $\mathbf { v}$ are given. Calculate the dot product $\mathbf { u } \cdot \mathbf { v }$. $\mathbf { u } = \langle 4,5 , - 6 \rangle$, $\mathbf { v } = \langle 0 , - 2 , - 3 \rangle$

Solution

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Answered 9 months ago
Answered 9 months ago
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Given that

$\boldsymbol{u} = \langle u_1,u_2,u_3 \rangle = \langle 4,5,-6 \rangle,$

$\boldsymbol{v} = \langle v_1,v_2,v_3 \rangle = \langle 0,-2,-3 \rangle.$

Substitute the vector components into the formula for the dot product:

\begin{aligned} \boldsymbol{u} \cdot \boldsymbol{v} &=& u_1 v_1 + u_2 v_2 + u_3 v_3 \\ &=& 4(0)+5(-2)+(-6)(-3) \\ &=& 0-10+18 \\ &=& 8 \end{aligned}

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