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JEE Advanced 2007Paper 1
Exam
JEE Advanced
Year
2007
Paper
Paper 1
Subject
Mathematics
Chapter
Vector Algebra

JEE Advanced 2007 · Paper 1 · Mathematics · Vector Algebra

Let the vectors P Q, Q R, R S, S T, T U and UP represent the sides...

Let the vectors PQ,QR,RS,ST,TU\mathbf{P Q}, \mathbf{Q R}, \mathbf{R S}, \mathbf{S T}, \mathbf{T U} and UP represent the sides of a regular hexagon. Statement I PQ ×(RS+ST)≠0\times(\mathbf{R S}+\mathbf{S T}) \neq \mathbf{0} Statement II PQ×RS=0\mathbf{P Q} \times \mathbf{R S}=\mathbf{0} and PQ×SQ≠0\mathbf{P Q} \times \mathbf{S Q} \neq \mathbf{0}Let the vectors P Q, Q R, R S, S T, T U and UP represent the sides of a regular hexagon. Statement I PQ ×(R S+S T) ≠ 0

Options

  1. AStatement I is true, Statement II is true; Statement II is a correct explanation for Statement I
  2. BStatement I is true, Statement II is true; Statement II is not a correct explanation for Statement I
  3. CStatement I is true, Statement II is false
  4. DStatement I is false, Statement II is true

Correct answer

C. Statement I is true, Statement II is false

Step-by-step solution

Since, PQ\mathbf{P Q} is not parallel to TR\mathbf{T R} ∵\because TR is resultant of SR\mathbf{S R} and ST\mathbf{S T} vectors. ⇒PQ×(RS+ST)≠0\Rightarrow \quad \mathbf{P Q} \times(\mathbf{R S}+\mathbf{S T}) \neq \mathbf{0} But for Statement II, we have PQ×RS=0\mathbf{P Q} \times \mathbf{R S}=\mathbf{0} which is not possible as PQ\mathbf{P Q} not parallel to RS\mathbf{R S}. Hence, Statement I is true and Statement II is false. Let the vectors P Q, Q R, R S, S T, T U and UP represent the sides of a regular hexagon. Statement I PQ ×(R S+S T) ≠ 0
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