Vector Algebra Question 181
Question: The value of ‘a’ so that the volume of parallelopiped formed by $ \mathbf{i}+a\mathbf{j}+\mathbf{k},\mathbf{j}+a,\mathbf{k} $ and $ a,\mathbf{i}+\mathbf{k} $ becomes minimum is
[IIT Screening 2003]
Options:
A) - 3
B) 3
C) $ \frac{1}{\sqrt{3}} $
D) $ \sqrt{3} $
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Answer:
Correct Answer: C
Solution:
- $ V=| ,\begin{matrix} 1 & a & 1 \\ 0 & 1 & a \\ a & 0 & 1 \\ \end{matrix}, |=1+a^{3}-a\Rightarrow \frac{dV}{da}=3a^{2}-1 $ $ =3,( a+\frac{1}{\sqrt{3}} ),( a-\frac{1}{\sqrt{3}} ) $
$ \therefore $ Minimum at $ \frac{1}{\sqrt{3}} $ .
BETA
