IIT-JEE 2007 · Paper 1 · Mathematics Q56

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MathematicsAssertion and reason+3 / -1Question 56 of 66

Let the vectors $\overrightarrow{PQ}$ , $\overrightarrow{QR}$ , $\overrightarrow{RS}$ , $\overrightarrow{ST}$ , $\overrightarrow{TU}$ and $\overrightarrow{UP}$ represent the sides of a regular hexagon.

STATEMENT-1: $\overrightarrow{PQ}\times\left(\overrightarrow{RS}+\overrightarrow{ST}\right)\ne\vec0$ .

because

STATEMENT-2: $\overrightarrow{PQ}\times\overrightarrow{RS}=\vec0$ and $\overrightarrow{PQ}\times\overrightarrow{ST}\ne\vec0$ .

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

Statement-1 is True, Statement-2 is False

Statement-1 is False, Statement-2 is True

Answer and worked solution

Official answer: C

Directions. Going round the regular hexagon, the sides $\overrightarrow{PQ},\overrightarrow{QR},\overrightarrow{RS},\overrightarrow{ST},\ldots$ point at $0°,60°,120°,180°,\ldots$ .

Statement 2. $\overrightarrow{RS}$ (at 120°) is not parallel to $\overrightarrow{PQ}$ , so $\overrightarrow{PQ}\times\overrightarrow{RS}\ne\vec0$ ; it is $\overrightarrow{ST}$ (at 180°) that is parallel, so $\overrightarrow{PQ}\times\overrightarrow{ST}=\vec0$ . Both parts are wrong: False.

Statement 1. $\overrightarrow{RS}+\overrightarrow{ST}=\overrightarrow{RT}$ , which points at 150° and is not parallel to $\overrightarrow{PQ}$ , so the cross product is nonzero: True.

(C)

Topics:Cross product

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IIT-JEE 2007 · Paper 1, Mathematics question 56