JEE Mains · Maths · STD 12 - 10. vector algebra
If the volume of a parallelopiped, whose coterminus edges are given by the vectors \(\overrightarrow{ a }=\hat{ i }+\hat{ j }+ n \hat{ k }, \quad \overrightarrow{ b }=2 \hat{ i }+4 \hat{ j }- n \hat{ k } \quad\) and \(\overrightarrow{ c }=\hat{ i }+ n \hat{ j }+3 \hat{ k } \quad( n \geq 0),\) is \(158 cu. Units\), then
- A \(\overrightarrow{ a } \cdot \overrightarrow{ c }=17\)
- B \(\overrightarrow{ b } \cdot \overrightarrow{ c }=10\)
- C \(n=7\)
- D \(n=9\)
Answer & Solution
Correct Answer
(B) \(\overrightarrow{ b } \cdot \overrightarrow{ c }=10\)
Step-by-step Solution
Detailed explanation
\(v =[\overrightarrow{ a } \overrightarrow{ b } \overrightarrow{ c }]\) \(158=\left|\begin{array}{ccc}1 & 1 & n \\ 2 & 4 & - n \\ 1 & n & 3\end{array}\right|, n \geq 0\) \(158=1\left(12+ n ^{2}\right)-(6+ n )+ n (2 n -4)\) \(\left[58= n ^{2}+12-6- n +2 n ^{2}-4 n \right.\)…
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