Q137 / 150 · MHT CET 2020 (16 Oct Shift 2) · Physics

The x, y components of vector $\overrightarrow{\mathrm{P}}$ have magnitudes 1 and 3 and the $\mathrm{x}, \mathrm{y}$ components of resultant of $\overrightarrow{\mathrm{P}}$ and $\overrightarrow{\mathrm{Q}}$ have magnitudes 5 and 6 respectively. What is the magnitude of $\overrightarrow{\mathrm{Q}}$ ?

  • A
    4
  • Correct answer
    B
    5
  • C
    3
  • D
    2

Solution

AS, $\quad \vec{P}=1 \hat{i}+3 \hat{j}-(i)$ And, $\vec{p}+\vec{Q}=5 \hat{i}+6 \hat{j}-(i i)$ $\therefore \vec{Q}=4 \hat{i}+3 \hat{j}$ $\begin{aligned} \therefore|\vec{Q}|=\sqrt{4^{2}+3^{2}}=\sqrt{16+9} &=\sqrt{25} \\ &=5 \end{aligned}$ option-2 correct

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

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