1.

ABCD is a quadrilateral. Forces \(\overrightarrow{AB}, \overrightarrow{CB}, \overrightarrow{CD}\) and \(\overrightarrow{DA}\) act along its sides. What is their resultant?1. \(2 \ \overrightarrow{CD}\)2. \(2 \ \overrightarrow{DA}\)3. \(2 \ \overrightarrow{BC}\)4. \(2 \ \overrightarrow{CB}\)

Answer» Correct Answer - Option 4 : \(2 \ \overrightarrow{CB}\)

Concept:

 A resultant force is the force (magnitude and direction) obtained when two or more forces are combined.

 

Calculations:

Given, ABCD is a quadrilateral. Forces \(\overrightarrow{AB}, \overrightarrow{CB}, \overrightarrow{CD}\) and \(\overrightarrow{DA}\) act along its sides.

⇒\(\vec {AB} = \vec b - \vec a\)

⇒\(\vec {CB} = \vec b - \vec c\)

⇒\(\vec {CD} = \vec d - \vec c\)

⇒\(\vec {DA} = \vec a - \vec d\)

 A resultant force is the force (magnitude and direction) obtained when two or more forces are combined.

Resultant Force =  \(\overrightarrow{AB} + \overrightarrow{CB} + \overrightarrow{CD}+\overrightarrow{DA}\) 

⇒Resultant Force = \(\rm \vec b - \vec a + \vec b - \vec c + \vec d - \vec c + \vec a - \vec d\)

⇒Resultant Force = \(\rm 2 \vec b - 2 \vec c\)

⇒Resultant Force = \(\rm 2 (\vec b - \vec c)\)

⇒Resultant Force = \(\rm 2\overrightarrow {CB}\)


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