Assertion A: If A, B, C, D are four points on a semi-circular arc… | JEE Main 2021 (27 Jul, Shift 1)

Q22JEE Main 2021 · 27 JUL · SHIFT 1Difficult

Addition & Subtraction of Vectors

Assertion A: If A, B, C, D are four points on a semi-circular arc with centre at 'O' such that , then $\overrightarrow{AB} + \overrightarrow{AC} + \overrightarrow{AD} = 4\overrightarrow{AO} + \overrightarrow{OB} + \overrightarrow{OC}$

Reason R: Polygon law of vector addition yields $\overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CD} + \overrightarrow{AD} = 2\overrightarrow{AO}$

In the light of the above statements, choose the most appropriate answer from the options given below:

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Answer: (a)

Write each vector through O: $\overrightarrow{AX} = \overrightarrow{AO} + \overrightarrow{OX}$ .
$\overrightarrow{AB} + \overrightarrow{AC} + \overrightarrow{AD} = 3\overrightarrow{AO} + \overrightarrow{OB} + \overrightarrow{OC} + \overrightarrow{OD}$ , and $\overrightarrow{OD} = \overrightarrow{AO}$ , giving $4\overrightarrow{AO} + \overrightarrow{OB} + \overrightarrow{OC}$ . A is correct.
Polygon law: $\overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CD} = \overrightarrow{AD} = 2\overrightarrow{AO}$ , so adding $\overrightarrow{AD}$ gives $4\overrightarrow{AO}$ , not $2\overrightarrow{AO}$ . R is wrong.
So the answer is (a).

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Addition & Subtraction of Vectors question from JEE Main 2021 (27 Jul, Shift 1)

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