JEE Advanced · Mathematics · 30. Vector Algebra
Let the vectors \(\mathbf{P Q}, \mathbf{Q R}, \mathbf{R S}, \mathbf{S T}, \mathbf{T U}\) and UP represent the sides of a regular hexagon.
Statement I PQ \(\times(\mathbf{R S}+\mathbf{S T}) \neq \mathbf{0}\)
Statement II \(\mathbf{P Q} \times \mathbf{R S}=\mathbf{0}\) and \(\mathbf{P Q} \times \mathbf{S Q} \neq \mathbf{0}\)
- A Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I
- B Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I
- C Statement I is true, Statement II is false
- D Statement I is false, Statement II is true
Answer & Solution
Correct Answer
(C) Statement I is true, Statement II is false
Step-by-step Solution
Detailed explanation
Since, \(\mathbf{P Q}\) is not parallel to \(\mathbf{T R}\)
\(\because\) TR is resultant of \(\mathbf{S R}\) and \(\mathbf{S T}\) vectors.
\(\Rightarrow \quad \mathbf{P Q} \times(\mathbf{R S}+\mathbf{S T}) \neq \mathbf{0}\)
But for Statement II, we have \(\mathbf{P Q} \times \mathbf{R S}=\mathbf{0}\)
which is not possible as \(\mathbf{P Q}\) not parallel to \(\mathbf{R S}\).
Hence, Statement I is true and Statement II is false.
\(\because\) TR is resultant of \(\mathbf{S R}\) and \(\mathbf{S T}\) vectors.
\(\Rightarrow \quad \mathbf{P Q} \times(\mathbf{R S}+\mathbf{S T}) \neq \mathbf{0}\)
But for Statement II, we have \(\mathbf{P Q} \times \mathbf{R S}=\mathbf{0}\)
which is not possible as \(\mathbf{P Q}\) not parallel to \(\mathbf{R S}\).
Hence, Statement I is true and Statement II is false.
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