Question

Vector A has magnitude 4.0 units and vector B has magnitude 6.0 units. The angle between A and B is 60.0°. What is the magnitude of 2A+3B ?

Answer 1

Find the components of A and B (assuming B points to positive direction of x-axis):

$$A_x=4\cos60°=2,\\ A_y=3.46,\\ \vec{A}=2\textbf{i}+3.46\textbf{j}\\ B_x=6,\\ B_y=0,\\ \vec{B}=6\textbf{i}.\\\space\\ 2\vec{A}=2·2\textbf{i}+2·3.46\textbf{j}=4\textbf{i}+6.92\textbf{j},\\ 3\vec{B}=18\textbf{i}.\\\space\\ \vec{R}=2\vec{A}+3\vec{B}=4\textbf{i}+6.92\textbf{j}+18\textbf{i}=22\textbf{i}+6.92\textbf{j}.\\\space\\ |\vec{R}|=\sqrt{(22)^2+(6.92)^2}{}=23.1.$$