Chapter 14.1, Problem 13WE

To determine

Sketchthe given expression using given vectors.

Explanation of Solution

Given:

The given vectors are

Vector $u\to$ magnitude $3$ and bearing ${315}^{°}$ .

Vector $v\to$ magnitude $2$ and bearing ${180}^{°}$ .

Vector $w\to$ magnitude $3$ and bearing ${90}^{°}$ .

  

The given expression is $u+2v-w$ .

Calculation:

Addition of two vectors $\to$ the sum or resultant of the vectors $u$ and $v$ can find by using either of the following two methods show that vector addition is commutative.

  $u+v=v+u$

First method $\to$ the triangle method

Second method $\to$ the parallelogram method

For the given vector $u+2v$ .

Vector $u\to$ magnitude $3$ and bearing ${315}^{°}$ .

  

Vector $v\to$ magnitude $2$ and bearing ${180}^{°}$ .

  

  $2v$ means just double the vector $v$ .

  

Vector $w\to$ magnitude $3$ and bearing ${90}^{°}$ .

  

The sketch (triangle method+ parallelogram method) of the vector $u+2v-w$ is given below.