Assertion A : If A, B, C, D are four points on a semi-circular are with centre at 'O' such that $\left| {\overrightarrow {AB} } \right| = \left| {\overrightarrow {BC} } \right| = \left| {\overrightarrow {CD} } \right|$, 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 :

Question

Assertion A
: If A, B, C, D are four points on a semi-circular are with centre at 'O' such that $\left| {\overrightarrow {AB} } \right| = \left| {\overrightarrow {BC} } \right| = \left| {\overrightarrow {CD} } \right|$, 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 :

A is correct but R is not correct.

A is not correct but R is correct.

Both A and R are correct and R is the correct explanation of A.

Both A and R are correct but R is not the correct explanation of A.

Solution

Please login to view the detailed solution steps...

Go to DASH