MHT CET · Physics · Mathematics in 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
- B 5
- C 3
- D 2
Answer & Solution
Correct Answer
(B) 5
Step-by-step Solution
Detailed explanation
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
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
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