Chapter 8.7, Problem 31PPS

To determine

To calculation:

Sum of given pair of vector.

Answer to Problem 31PPS

Sum of given pair of vector $\langle a,b\rangle +\langle c,d\rangle$ is $\langle a+b,c+d\rangle$ .

Explanation of Solution

Given information:

  $\langle a,b\rangle +\langle c,d\rangle$ .

Calculation:

Given vectors are $\langle a,b\rangle +\langle c,d\rangle$ .

Let,

  $\begin{array}{l}\stackrel{\rightharpoonup }{x}=\langle a,b\rangle \\ \stackrel{\rightharpoonup }{y}=\langle c,d\rangle \end{array}$

Add the two vectors by adding each coordinate component together,

  $\begin{array}{l}\langle x_1,y_1\rangle \langle x_2,y_2\rangle =\langle x_1+x_1,y_2+y_2\rangle \\ =\langle a+b,c+d\rangle \end{array}$

Hence, Sum of given pair of vector $\langle a,b\rangle +\langle c,d\rangle$ is $\langle a+b,c+d\rangle$ .