Mathematics in Physics

JEE Main level, single correct, medium

30 of 121

Question 30 of 121

In an octagon ABCDEFGHABCDEFGH of equal side, what is the sum of AB⃗+AC⃗+AD⃗+AE⃗+AF⃗+AG⃗+AH⃗,\vec{AB}+\vec{AC}+\vec{AD}+\vec{AE}+\vec{AF}+\vec{AG}+\vec{AH}, if, AO⃗=2i^+3j^−4k^\vec{AO}=2\hat{i}+3\hat{j}-4\hat{k}

Show answer and solution

Answer: (A) 16i^+24j^−32k^16\hat{i}+24\hat{j}-32\hat{k}

We know,
∵OA⃗+OB⃗+OC⃗+OD⃗+OE⃗+OF⃗+OG⃗+OH⃗=0⃗∵\vec{OA}+\vec{OB}+\vec{OC}+\vec{OD}+\vec{OE}+\vec{OF}+\vec{OG}+\vec{OH}=\vec{0}
By triangle law of vector addition, we can write
AB⃗=AO⃗+OB⃗;AC⃗=AO⃗+OC⃗\vec{AB}=\vec{AO}+\vec{OB};\vec{AC}=\vec{AO}+\vec{OC}
AD⃗=AO⃗+OD⃗;AE⃗=AO⃗+OE⃗\vec{AD}=\vec{AO}+\vec{OD};\vec{AE}=\vec{AO}+\vec{OE}
AF⃗=AO⃗+OF⃗;AG⃗=AO⃗+OG⃗\vec{AF}=\vec{AO}+\vec{OF};\vec{AG}=\vec{AO}+\vec{OG}
AH⃗=AO⃗+OH⃗\vec{AH}=\vec{AO}+\vec{OH}
Now
AB⃗+AC⃗+AD⃗+AE⃗+AF⃗+AG⃗+AH⃗\vec{AB}+\vec{AC}+\vec{AD}+\vec{AE}+\vec{AF}+\vec{AG}+\vec{AH}
=(7AO⃗)+OB⃗+OC⃗+OD⃗+OE⃗+OF⃗+OG⃗+OH⃗=\left(7\vec{AO}\right)+\vec{OB}+\vec{OC}+\vec{OD}+\vec{OE}+\vec{OF}+\vec{OG}+\vec{OH}
=(7AO⃗)+0⃗−OA⃗=\left(7\vec{AO}\right)+\vec{0}-\vec{OA}
=(7AO⃗)+AO⃗=\left(7\vec{AO}\right)+\vec{AO}
=8AO⃗=8(2i^+3j^−4k^)=8\vec{AO}=8\left(2\hat{i}+3\hat{j}-4\hat{k}\right)
=16i^+24j^−32k^=16\hat{i}+24\hat{j}-32\hat{k}

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.

More Physics practice

JEE Main Physics practice question on Mathematics in Physics (Addition and Subtraction of Vectors), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.