Let the vectors \(\overrightarrow{P Q}, \overrightarrow{Q R}, \overrightarrow{R S}, \overrightarrow{S T}, \overrightarrow{T U}\) and \(\overrightarrow{U P}\) represent the sides of a regular hexagon. STATEMENT-1 : \(\overrightarrow{P Q} \times(\overrightarrow{R S}+\overrightarrow{S T}) \neq \overrightarrow{0}\). because STATEMENT-2 : \(\overrightarrow{P Q} \times \overrightarrow{R S}=\overrightarrow{0}\) and \(\overrightarrow{P Q} \times \overrightarrow{S T} \neq \overrightarrow{0}\).

(C) Statement-1 is True, Statement-2 is False

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

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

(D) Statement-1 is False, Statement-2 is True

JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Vector Algebra

Let the vectors

P Q, QR, R S, S T, T U

and

U P

represent the sides of a regular hexagon.

STATEMENT-1 :

P Q \times (R S + S T) \neq = 0

.

because

STATEMENT-2 :

P Q \times R S = 0

and

P Q \times S T \neq = 0

(A)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C)Statement-1 is True, Statement-2 is False✓ Correct
(D)Statement-1 is False, Statement-2 is True

Answer: (C)

Solution

In a regular hexagon,

P Q

is parallel to

T R

(where

T R = R S + S T

).

Since

P Q ∥ T R

, we have

P Q \times (R S + S T) \neq = 0

(they are parallel but not necessarily equal in magnitude and direction for the cross product to be zero in this context).

Actually, in a regular hexagon,

P Q

is NOT parallel to

R S

, so

P Q \times R S \neq = 0

.

Statement-2 claims

P Q \times R S = 0

, which is False.

Statement-1 is True because the resultant

R S + S T

is not parallel to

P Q

JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Single correct option

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JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Vector Algebra

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