JEE PYQ: Mathematics In Physics Question 5
Question 5 - 2021 (25 Feb Shift 1)
In an octagon ABCDEFGH of equal side, what is the sum of $\vec{AB} + \vec{AC} + \vec{AD} + \vec{AE} + \vec{AF} + \vec{AG} + \vec{AH}$
If, $\vec{AO} = 2\hat{i} + 3\hat{j} - 4\hat{k}$
(1) $16\hat{i} + 24\hat{j} - 32\hat{k}$
(2) $-16\hat{i} - 24\hat{j} - 32\hat{k}$
(3) $-16\hat{i} - 24\hat{j} + 32\hat{k}$
(4) $-16\hat{i} + 24\hat{j} + 32\hat{k}$
Show Answer
Answer: (1)
Solution
$\vec{AO} + \vec{OB} = \vec{AB}$ $\vec{AO} + \vec{OC} = \vec{AC}$ $\vec{AO} + \vec{OD} = \vec{AD}$ $\vec{AO} + \vec{OE} = \vec{AE}$ $\vec{AO} + \vec{OF} = \vec{AF}$ $\vec{AO} + \vec{OG} = \vec{AG}$ $\vec{AO} + \vec{OH} = \vec{AH}$ $8\vec{AO} = (\vec{AB} + \vec{AC} + \vec{AD} + \vec{AE} + \vec{AF} + \vec{AG} + \vec{AH})$ $= 8(2\hat{i} + 3\hat{j} - 4\hat{k})$ $= 16\hat{i} + 24\hat{j} - 32\hat{k}$
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