The value of $a$ so that the volume of parallelopiped formed by $\widehat {\bf{i}} + a\widehat {\bf{j}} + {\bf{\hat k}},\;\widehat {\bf{j}} + a{\bf{\hat k}}$ and $a\widehat {\bf{i}} + {\bf{\hat k}}$ becomes minimum is

JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

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The value of

a

so that the volume of parallelopiped formed by

\widehat \mathbf{i} + a\widehat \mathbf{j} + \mathbf{\hat k},\;\widehat \mathbf{j} + a\mathbf{\hat k}

and

a\widehat \mathbf{i} + \mathbf{\hat k}

becomes minimum is

View answer and explanation

Correct option: C

1/\sqrt 3

Option C (

1/\sqrt 3

) is correct because it minimizes the volume of the parallelepiped, which is found by taking the derivative and setting it to zero.

Practice All Chapter MCQs →

\vec r\cdot\vec a = \vec r\cdot\vec b = \vec r\cdot\vec c = 0

\vec r,

\left[ {\vec a\vec b\vec c} \right],

\frac{{x - 3}}{2} = \frac{{y - 2}}{3} = \frac{{z - 1}}{{ - 1}}

\frac{{x + 3}}{2} = \frac{{y - 6}}{1} = \frac{{z - 5}}{3},

\mathbf{\vec a} = \widehat \mathbf{i} - \mathbf{\hat k},\;\mathbf{\vec b} = x\widehat \mathbf{i} + \widehat \mathbf{j} + \left( {1 - x} \right)\mathbf{\hat k}

\mathbf{\vec c} = y\widehat \mathbf{i} + x\widehat \mathbf{j} + \left( {1 + x - y} \right)\mathbf{\hat k}.

\left[ {\mathbf{\vec a},\;\mathbf{\vec b},\;\mathbf{\vec c}} \right]

\vec{a}, \vec{b}

((\vec{a} \times \vec{b}) \times \vec{a}) \cdot((\vec{b} \times \vec{a}) \times \vec{b})

a \cdot(a \times b)=

\mathbf{r}=\mathbf{b}+\lambda \mathbf{c}