Q216 / 270 · NDA 2018 (Phase 2) · Mathematics

If $|\vec{a}|=3,|\vec{b}|=4$ and $|\vec{a}-\vec{b}|=5$, then what is the value of $|\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}|=$ ?

  • A
    8
  • B
    6
  • C
    $5 \sqrt{2}$
  • Correct answer
    D
    5

Solution

$\begin{aligned} &|\vec{a}+\vec{b}|^2+|\vec{a}-\vec{b}|^2=2\left\{|\vec{a}|^2+|\vec{b}|^2\right\}=2 \times 25=50 \\ & \Rightarrow|\vec{a}+\vec{b}|^2+25=50 \\ & \Rightarrow|\vec{a}+\vec{b}|^2=25 \\ & \Rightarrow|\vec{a}+\vec{b}|=5\end{aligned}$

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

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