Mathematics - Vector Question with Solution | TestHub

MathematicsVectorGeneral definitions, Angle between vectors, Section formula, Geometrical resultsMedium2 minPYQ_2002

MathematicsMediumsingle choice

The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12 N. The magnitude of the two forces are

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Solution:

Let two forces be $P$ and $Q$ . Given $P + Q = 18$ and $P \overset{a}{^} + Q \hat{b} = 12 \overset{c}{^} \Rightarrow P \overset{a}{^} - 12 \overset{c}{^} = \overset{ˉ}{Q} \hat{b}$ $\Rightarrow P^{2} + 144 = Q^{2} = (18 - P)^{2}; \Rightarrow P^{2} + 144 = 324 - 36 P + P^{2} \Rightarrow 36 P = 180 \Rightarrow P = 5 and Q = 13$ (where $a$ and $b$ are unit vectors along $P$ and $Q$ ).

Stream:JEESubject:MathematicsTopic:VectorSubtopic:General definitions, Angle between vectors, Section formula, Geometrical results

⏱ 2mℹ️ Source: PYQ_2002

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