\(..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep."> If the volume of a parallelepiped whose adjacent edges are
\(..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep." /> If the volume of a parallelepiped whose adjacent edges are
\(..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep." />
<p>If the volume of a parallelepiped whose adjacent edges are</p>
<p><span class="math-tex">\(\rm \vec a\)</span> = 2î + 3ĵ + 4k̂</p>
<p><span class="math-tex">\(\rm \vec b\)</span> = î + αĵ + 2k̂</p>
<p><span class="math-tex">\(\rm \vec c\)</span> = î + 2ĵ + αk̂</p>
<p>is 15 then α = ?</p>
Step-by-step Solution: Volume:
\[
\left| \begin{array}{ccc} 2 & 3 & 4 \\ 1 & \alpha & 2 \\ 1 & 2 & \alpha \end{array} \right| = 15
\]
\[
\Rightarrow 2(\alpha^2 - 4) - 3(\alpha - 2) + 4(2 - \alpha) = 15
\]
\[
\Rightarrow 2\alpha^2 - 7\alpha - 9 = 0
\]
\[
\Rightarrow (\alpha + 1)(2\alpha - 9) = 0
\]
Hence:
\[
\alpha = -1, \quad \frac{9}{2}
\]Question 37
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