Question

Given that vector A=2i+5j-6k and Vector B=3i-6j+5k, what is the magnitude of the resultant vector R=A+B

Answer 1

The vectors A and B have three components. Thus, to find the components of the resultant vector, we can add each component respectively:

$$\textbf{R}=\textbf{A}+\textbf{B}=\\ =(2\textbf{i}+5\textbf{j}-6\textbf{k})+(3\textbf{i}-6\textbf{j}+5\textbf{k})=\\ =(2+3)\textbf{i}+(5-6)\textbf{j}+(-6+5)\textbf{k}=\\ =5\textbf{i}-\textbf{j}-\textbf{k}.$$

The magnitude of the resultant will be

$$|\textbf{R}|=\sqrt{5^2+(-1)^2+(-1)^2}=5.2.$$