Question

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

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

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

Accepted Answer

(C) Both $\mathbf{A}$ and $\mathbf{R}$ are correct and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$.

Answer

(A) $\mathbf{A}$ is not correct but $\mathbf{R}$ is correct.

Answer

(B) $\mathbf{A}$ is correct but $\mathbf{R}$ is not correct.

Answer

(D) Both $\mathbf{A}$ and $\mathbf{R}$ are correct but $\mathbf{R}$ is not the correct explanation of A.

JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Vector

Solution

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