Answer:
Magnitude of vector A = 0.904
Explanation:
Vector A , which is directed along an x axis, that is
[tex]\vec{A}=x_A\hat{i}[/tex]
Vector B , which has a magnitude of 5.5 m
[tex]\vec{B}=x_B\hat{i}+y_B\hat{j}[/tex]
[tex]\sqrt{x_{B}^{2}+y_{B}^{2}}=5.5\\\\x_{B}^{2}+y_{B}^{2}=30.25[/tex]
The sum is a third vector that is directed along the y axis, with a magnitude that is 6.0 times that of vector A [tex]\vec{A}+\vec{B}=6x_A\hat{j}\\\\x_A\hat{i}+x_B\hat{i}+y_B\hat{j}=6x_A\hat{j}[/tex]
Comparing we will get
[tex]x_A=-x_B\\\\y_B=6x_A[/tex]
Substituting in [tex]x_{B}^{2}+y_{B}^{2}=30.25[/tex]
[tex]\left (-x_{A} \right )^{2}+\left (6x_{A} \right )^{2}=30.25\\\\37x_{A}^2=30.25\\\\x_{A}=0.904[/tex]
So we have
[tex]\vec{A}=0.904\hat{i}[/tex]
Magnitude of vector A = 0.904
