The magnitude of the $X$ and $Y$ components of $\overrightarrow{A}\ $are 7 and 6. Also the magnitudes of $X$ and $Y$ components of $\overrightarrow{A} + \overrightarrow{B}$ are 11 and 9 respectively. What is the magnitude of $\overrightarrow{B}$?

Question

Dr. Abubacker · Accepted Answer

(a) Let $\overrightarrow{A} + \overrightarrow{B}$=$\overrightarrow{R}$. Given $A_{x}$=7 and $A_{y} = 6$
Also $R_{x} = 11$ and $R_{y}$=9. Therefore,
$B_{x} = R_{x} - A_{x} = 11 - 7 = 4$
and $B_{y} = R_{y} - A_{y} = 9 - 6 = 3$
Hence, $B = \sqrt{B_{x}^{2} + B_{y}^{2}} = \sqrt{4^{2} + 3^{2}} = 5$

Q. The magnitude of the $X$ and $Y$ components of $\overrightarrow{A}\ $are 7 and 6. Also the magnitudes of $X$ and $Y$ components of $\overrightarrow{A} + \overrightarrow{B}$ are 11 and 9 respectively. What is the magnitude of $\overrightarrow{B}$?

Explanation

Reviewed by Dr. Abubacker

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