Let $\vec{P}=\left(p_{1}, p_{2}, p_{3}\right)$ give the profit a salesman makes from selling three different models of computers. Let $\vec{S}=\left(s_{1}, s_{2}, s_{3}\right)$ give the number of each computer model sold each week. What does $\vec{P} \cdot \vec{S}$ represent?
A) A scalar giving the total profit for one week from selling all three models of computers.
B) A scalar giving the average profit for one week from selling each computer model.
C) A vector giving the profit for one week for the three models of computers.
D) A vector giving the average profit for one week for the three models of computers.

Question

Quizplus · Accepted Answer

$\vec{P} \cdot \vec{S}$ is a scalar that represents the total profit for one week from selling all three models of computers. This is because the dot product of two vectors is a scalar that is equal to the sum of the products of the corresponding components of the vectors. In this case, the corresponding components of $\vec{P}$ and $\vec{S}$ are the profits and the number of computers sold for each model, respectively. Therefore, the dot product of $\vec{P}$ and $\vec{S}$ is equal to the total profit for one week from selling all three models of computers.

Let P⃗=(p1,p2,p3)\vec{P}=\left(p_{1}, p_{2}, p_{3}\right)P=(p1​,p2​,p3​) Give the Profit a Salesman Makes from Selling Three Different

Let $\vec{P}=\left(p_{1}, p_{2}, p_{3}\right)$ Give the Profit a Salesman Makes from Selling Three Different