If $\widehat {\bf{i}} - {\bf{\hat k}},\;{\rm{\lambda \;}}\widehat {\bf{i}} + \widehat {\bf{j}} + \left( {1 - \lambda } \right){\bf{\hat k}}$ and ${\rm{\mu }}\;\widehat {\bf{i}} + {\rm{\lambda \;}}\widehat {\bf{j}} + \left( {1 + {\rm{\lambda \;}}\widehat {\bf{j}} - {\rm{\mu }}} \right){\bf{\hat k}}$ are three coterminal edges of a parallelopiped, then its volume depends on

JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

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\widehat \mathbf{i} - \mathbf{\hat k},\;\mathrm{\lambda \;}\widehat \mathbf{i} + \widehat \mathbf{j} + \left( {1 - \lambda } \right)\mathbf{\hat k}

and

\mathrm{\mu }\;\widehat \mathbf{i} + \mathrm{\lambda \;}\widehat \mathbf{j} + \left( {1 + \mathrm{\lambda \;}\widehat \mathbf{j} - \mathrm{\mu }} \right)\mathbf{\hat k}

are three coterminal edges of a parallelopiped, then its volume depends on

View answer and explanation

Correct option: D

Neither λ nor μ

Option D is correct because the volume of the parallelepiped is independent of both λ and μ, and is equal to 1.

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}