The magnitudes of the x and y components of P- are 7 and 6- The magnitudes of the x and y components of P-Q- are 11 and 9- respectively- What is the magnitude of Q-

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Byju's Answer

Standard XII

Physics

Vector Addition

The magnitude...

Question

The magnitudes of the $x$ and $y$ components of $\to P$ are $7$ and $6$ . The magnitudes of the $x$ and $y$ components of $\to P + \to Q$ are $11$ and $9$ , respectively. What is the magnitude of $Q$ ?

9

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6

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5

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Solution

The correct option is D $5$
Let $\to R = \to P + \to Q$
${∣ ∣ \to P ∣ ∣}_{x} = 7, {∣ ∣ \to P ∣ ∣}_{y} = 6$ $& {∣ ∣ \to R ∣ ∣}_{x} = 11, {∣ ∣ \to R ∣ ∣}_{y} = 9$
$R_{x} = P_{x} + Q_{x} o r 11 - 7 = Q_{x} o r Q_{x} = 4 R_{y} {= P}_{y} + Q_{y} o r 9 - 6 = Q_{y} o r Q_{y} = 3 Q = \sqrt{4^{2} + 3^{2}} = 5$

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The magnitudes of the x and y components of →P are 7 and 6. The magnitudes of the x and y components of →P+→Q are 11 and 9, respectively. What is the magnitude of Q?

The correct option is D 5Let →R=→P+→Q∣∣→P∣∣x=7,∣∣→P∣∣y=6&∣∣→R∣∣x=11,∣∣→R∣∣y=9Rx=Px+Qxor11−7=QxorQx=4Ry=Py+Qyor9−6=QyorQy=3Q=√42+32=5

The magnitudes of the $x$ and $y$ components of $\to P$ are $7$ and $6$ . The magnitudes of the $x$ and $y$ components of $\to P + \to Q$ are $11$ and $9$ , respectively. What is the magnitude of $Q$ ?