Question
Find $\vec{a} \cdot \vec{b}$ and the angle between $\vec{a}$ and $\vec{b}$ when they are tail-to-tail.$$\begin{aligned}&\vec{a}=2 \vec{\imath}+5 \vec{j}+3 \vec{k}\\&\vec{b}=7 \vec{\imath}-\vec{j}+4 \vec{k}\end{aligned}$$
Step 1
The dot product of two vectors is calculated as the sum of the products of their corresponding components. So, we have: \[\vec{a} \cdot \vec{b} = (2 \cdot 7) + (5 \cdot -1) + (3 \cdot 4) = 14 - 5 + 12 = 21\] Show more…
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