Chapter 6, Problem 10CT

(a)

To determine

To find: The value of expression $2v+u$ .

Answer to Problem 10CT

The value of $2v+u$ is $\langle 1,8\rangle$ .

Explanation of Solution

Given:

The value of the points are $u=\langle -7,-4\rangle$ and $v=\langle 4,6\rangle$ .

Calculation:

Consider the given equation is,

  $2v+u$

Then, the above equation with the given points is,

  $\begin{array}{c}2v+u=2\langle 4,6\rangle +\langle -7,-4\rangle \\ =\langle 8,12\rangle +\langle -7,-4\rangle \\ =\langle 8+\left(-7\right),12+\left(-4\right)\rangle \\ =\langle 1,8\rangle \end{array}$

(b)

To determine

To find: The value of expression $u-3v$ .

Answer to Problem 10CT

The value of $u-3v$ is $\langle -19,-22\rangle$ .

Explanation of Solution

Given:

The value of the points are $u=\langle -7,-4\rangle$ and $v=\langle 4,6\rangle$ .

Calculation:

Consider the given equation is,

  $u-3v$

Then, the above equation with the given points is,

  $\begin{array}{c}u-3v=\langle -7,-4\rangle -3\langle 4,6\rangle \\ =\langle -7,-4\rangle +\langle -12,-18\rangle \\ =\langle -7+\left(-12\right),-18+\left(18\right)\rangle \\ =\langle -19,-22\rangle \end{array}$

(c)

To determine

To find: The value of expression $5u-4v$ .

Answer to Problem 10CT

The value of $5u-4v$ is $\langle -51,-44\rangle$ .

Explanation of Solution

Given:

The value of the points are $u=\langle -7,-4\rangle$ and $v=\langle 4,6\rangle$ .

Calculation:

Consider the given equation is,

  $u-3v$

Then, the above equation with the given points is,

  $\begin{array}{c}5u-4v=5\langle -7,-4\rangle -4\langle 4,6\rangle \\ =\langle -35,-20\rangle -\langle 16,24\rangle \\ =\langle -35+\left(-16\right),-20+\left(-24\right)\rangle \\ =\langle -51,-44\rangle \end{array}$