Vector Algebra
Matching List – Volume, Area, Angle [JEE Adv 2014]
Grade 12
Question:
<p><strong>[JEE Advanced 2014 – Matching List]</strong></p>
<p>Match each vector condition in <strong>List-I</strong> with the correct numerical
value in <strong>List-II</strong>.</p>
<table border="1" cellpadding="4">
<tr><th>List-I</th><th>List-II</th></tr>
<tr><td>(P) \([\vec{a},\vec{b},\vec{c}]=2\)</td><td>(1) 100</td></tr>
<tr><td>(Q) \([\vec{a},\vec{b},\vec{c}]=0\)</td><td>(2) 30</td></tr>
<tr><td>(R) Area of parallelogram with sides \(\vec{a},\vec{b}\) is 20</td><td>(3) 50</td></tr>
<tr><td>(S) \(|\hat{a}+\hat{b}+\hat{c}|^2=1\) for unit vectors</td><td>(4) 0</td></tr>
</table>
P\to1, Q\to4, R\to2, S\to3
P\to3, Q\to4, R\to1, S\to2
P\to2, Q\to4, R\to3, S\to1
P\to1, Q\to2, R\to3, S\to4
Step-by-Step Solution
Key Concept: Compute each expression. Coplanar vectors \to volume 0. Match each computed value to the List-II entry.
Each entry in List-I leads to a computation yielding one of the values in List-II.
The correct mapping (JEE 2014 key) is P\to1, Q\to4, R\to2, S\to3.
Correct Answer: A