Q202 / 270 · NDA 2013 (Phase 2) · Mathematics

The position vectors of the points $A$ and $B$ are respectively $3 \hat{i}-5 \hat{j}+2 \hat{k}$ and $\hat{i}+\hat{j}-\hat{k}$. What is the length of $A B$ ?

  • A
    11
  • B
    9
  • Correct answer
    C
    7
  • D
    6

Solution

$\begin{aligned} \overrightarrow{\mathrm{AB}} & =(3-1) \hat{i}+(-5-1) \hat{j}+(2-(-1)) \hat{k} \\ & =2 \hat{i}-6 \hat{j}+3 \hat{k} \\ |\overrightarrow{\mathrm{AB}}| & =\sqrt{(2)^2+(-6)^2+(3)^2} \\ & =\sqrt{4+36+9}=\sqrt{49}=7 \text { units. }\end{aligned}$

Hence, the correct answer is option: 'C'.

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