Question

If $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C}$ and $|\overrightarrow{C}{|}_{max}=12,|\overrightarrow{C}{|}_{min}=8$. Then find the value of $|\overrightarrow{A}|$ and $|\overrightarrow{B}|$.

• A. $|\overrightarrow{A}|=2,|\overrightarrow{B}|=5$
• B. $|\overrightarrow{A}|=10,|\overrightarrow{B}|=2$
• C. $|\overrightarrow{A}|=2,|\overrightarrow{B}|=10$
• D. $|\overrightarrow{A}|=5,|\overrightarrow{B}|=10$

Answer 1

Answer: (B), (C)

$|\overrightarrow{A}|=2,|\overrightarrow{B}|=10$

We can write,
$\begin{array}{}{C}_{max}=12=A+B& \text{(1)}\end{array}$
$|\overrightarrow{C}{|}_{min}=8$
Case 1: $A>B$
$\begin{array}{}A-B=8& \text{(2)}\end{array}$
Solving $\left(1\right)$ and $\left(2\right)$
$A=10$, $B=2$
Case 2: $B>A$
$\begin{array}{}B-A=8& \text{(3)}\end{array}$
Solving $\left(2\right)$ and $\left(3\right)$
$A=2$, $B=10$