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3-1.Vectors
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The magnitude of the $X$ and $Y$ component of $\vec A$ are $7$ and $6$ respectively. Also the magnitude of $X$ and $Y$ component of $\vec A + \vec B$ are $11$ and $9$ respectively. What is the magnitude of $\vec B$ ?
A
$5$
B
$6$
C
$8$
D
$9$
Solution
Let $\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{R}}$
Given $A_{x}=7$ and $A_{y}=6$
$\mathrm{R}_{\mathrm{x}}=11$ and $\mathrm{R}_{\mathrm{y}}=9$
$\begin{aligned} \therefore \mathrm{B}_{\mathrm{x}}=\mathrm{R}_{\mathrm{x}}-\mathrm{A}_{\mathrm{x}} \\=11-7=4 \\ \mathrm{B}_{\mathrm{y}}=\mathrm{R}_{\mathrm{y}}-\mathrm{A}_{\mathrm{y}}=9-6 &=3 \\ \mathrm{B}=\sqrt{\mathrm{B}_{\mathrm{x}}^{2}+\mathrm{B}_{\mathrm{y}}^{2}} \\=\sqrt{4^{2}+3^{2}}=5 \end{aligned}$
Standard 11
Physics
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