JEE MATHEMATICS MCQ: SCALAR TRIPLE PRODUCT

1 Easy

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Analyzing +4 | -1

Let

G_1, G_2, G_3

be the centroids of the triangular faces

O B C, O C A, O A B

of a tetrahedron

O A B C

. If

V_1

denote the volume of the tetrahedron

\mathrm{OABC}

and

V_2

that of the parallelopiped with

O G_1, O G_2, O G_3

as three concurrent edges, then

View answer and explanation

Correct option: A

4 V_1=9 V_2

Option A (

4 V_1=9 V_2

) is correct because it relates the volume of the tetrahedron to the volume of the parallelepiped formed by the centroids of its faces.

More Questions from SCALAR TRIPLE PRODUCT

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

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

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\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}