Question

Let and be nonzero vectors in the

plane, and let $\theta$ be the angle between them.

a) The dot product of u and v is defined by u.v = ____________

The dot product of two vectors is a _______________, not a vector.

Short answer

The product of two vectors having $\theta$ angle between them is $u·v=\left|u\right|\left|v\right|\cos \theta$

The dot product of two vectors is a number, not a vector.

Step-by-step solution

Step 1. Given information.

$\begin{array}{l}u=〈a_1,a_2〉\\ v=〈b_1,b_2〉\end{array}$

Step 2. Determining the dot product.

$\begin{array}{l}u=〈a_1,a_2〉\\ v=〈b_1,b_2〉\end{array}$

Since $\theta$is the angle between the vectors, then

$u·v=\left|u\right|\left|v\right|\cos \theta$

After the dot product of two vectors, we get the number as the result and not the vector. Therefore, the dot product of two vector is a number, not a vector.