Chapter 14.5, Problem 1MRE

To determine

To find: the value of $\text{w}$ in the component form if summation of $\text{u and v}$ gives $\text{w}$ .

Answer to Problem 1MRE

  $\text{w=u+v=5i-3j}$ .

Explanation of Solution

Given:

  $\text{u=3i+j}$ and $\text{v=2i-4j}$ .

Concept used:

The component form of the vector is the ordered pair that describes the changes in the $\text{x and y}$ values.

Let the initial point $\text{P}\left({\text{p}}_{\text{1}}{\text{,p}}_{\text{2}}\right)$ and the terminal point $Q\left(q_{\text{1}}{\text{,q}}_{\text{2}}\right)$ the component for the vector $\text{PQ}$ is given by:

  $\overrightarrow{\text{PQ}}\text{=}\left({\text{q}}_{\text{1}}{\text{-p}}_{\text{1}}{\text{,q}}_{\text{2}}{\text{-p}}_{\text{2}}\right)$ .

The magnitude of the vector $\text{PQ}$ is given by distance formula:

  $\Vert \text{PQ}\Vert \text{=}\sqrt{{\left({\text{q}}_{\text{1}}{\text{-p}}_{\text{1}}\right)}^2\text{+}{\left({\text{q}}_{\text{2}}{\text{-p}}_{\text{2}}\right)}^2}$ .

Calculation:

According to the given equation:

  $\text{u=3i+j}$ and $\text{v=2i-4j}$ .

  $\text{w=u+v}$ is

  $\text{w=3i+j+2i-4j}$ .

Same unit vector will add up.

  $\text{w=5i-3j}$ .

Hence, $\text{w=u+v=5i-3j}$ .