Question

Find the magnitude of the vector which joins the point $A$$(a,2,c)$ to $B$$(a+1,5,c+3)$.

• A. $\sqrt{18}$
• B. $\sqrt{21}$
• C. $\sqrt{20}$
• D. None of these

Answer 1

Answer: (D)

None of these

Given points

$A(a,2,c)$ and $B(a+1,5,c+3)$

$\overrightarrow{OA}=a\hat{i}+2\hat{j}+c\hat{k}$

$\overrightarrow{OB}=(a+1)\hat{i}+5\hat{j}+(c+3)\hat{j}$

$\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}$

$\overrightarrow{AB}=(a+1)\hat{i}+5\hat{j}+(c+3)\hat{j}-(a\hat{i}+2\hat{j}+c\hat{k})$

$\overrightarrow{AB}=a\hat{i}+5\hat{j}+c\hat{k}+\hat{i}+3\hat{j}-a\hat{i}-2\hat{j}-c\hat{k}$

$\overrightarrow{AB}=\hat{i}+3\hat{j}+3\hat{j}$

magnitude of AB

$\left|\overrightarrow{AB}\right|=\sqrt{1^2+3^2+3^2}$

$\left|\overrightarrow{AB}\right|=\sqrt{1+9+9}$

$\left|\overrightarrow{AB}\right|=\sqrt{19}$

none of option is matched