Assertion A: If A, B, C, D are four points on a semi-circular arc with centre at O such that |AB⃗| = |BC⃗| = |CD⃗|, then AB⃗ + AC⃗ + AD⃗ = 4AO⃗ + OB⃗ + OC⃗. Reason R: Polygon law of vector addition yields AB⃗ + BC⃗ + CD⃗ = AD⃗ = 2AO⃗. In the light of the above statements, choose the most appropriat…

Question

Assertion A: If A, B, C, D are four points on a semi-circular arc with centre at O such that |AB⃗| = |BC⃗| = |CD⃗|, then AB⃗ + AC⃗ + AD⃗ = 4AO⃗ + OB⃗ + OC⃗. Reason R: Polygon law of vector addition yields AB⃗ + BC⃗ + CD⃗ = AD⃗ = 2AO⃗. In the light of the above statements, choose the most appropriate answer from the options given below.

Accepted Answer

(2) Both A and R are correct but R is not the correct explanation of A.. Split each vector through O: AB⃗ = AO⃗ + OB⃗, AC⃗ = AO⃗ + OC⃗, AD⃗ = AO⃗ + OD⃗. O is the midpoint of the diameter AD, so OD⃗ = AO⃗. Sum = 3AO⃗ + OB⃗ + OC⃗ + AO⃗ = 4AO⃗ + OB⃗ + OC⃗: A is correct. Polygon law: AB⃗ + BC⃗ + CD⃗ = AD⃗ = 2AO⃗: R is correct, but it is a different statement and does not produce A.

Step-by-step solution

Why the other options are wrong