Volume of a parallelepiped with coterminous e | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The volume of a parallelepiped with coterminous edges $\vec{a}, \vec{b}, \vec{c}$ is given by the scalar triple product $[\vec{a} \vec{b} \vec{c}]

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) The volume of a parallelepiped with coterminous edges $\vec{a}, \vec{b}, \vec{c}$ is given by the scalar triple product $[\vec{a} \vec{b} \vec{c}] = 12$.The volume of a tetrahedron with coterminous edges $\vec{u}, \vec{v}, \vec{w}$ is given by $V = \frac{1}{6} |[\vec{u} \vec{v} \vec{w}]|$.Here,$\vec{u} = \vec{a} - \vec{b}$,$\vec{v} = \vec{b} - \vec{c}$,and $\vec{w} = \vec{a} + \vec{b} - \vec{c}$.Calculating the scalar triple product $[\vec{u} \vec{v} \vec{w}] = [(\vec{a} - \vec{b}) (\vec{b} - \vec{c}) (\vec{a} + \vec{b} - \vec{c})]$.Using the properties of the scalar triple product,this simplifies to:$[\vec{a} - \vec{b}, \vec{b} - \vec{c}, \vec{a} + \vec{b} - \vec{c}] = [\vec{a} \vec{b} \vec{c}] = 12$.Therefore,the volume of the tetrahedron is $\frac{1}{6} 	imes 12 = 2$ cubic units.

Volume of a parallelepiped with coterminous edges $\vec{a}, \vec{b}, \vec{c}$ is $12$ cubic units. The volume of a tetrahedron with coterminous edges $\vec{a} - \vec{b}, \vec{b} - \vec{c}, \vec{a} + \vec{b} - \vec{c}$ will be ............. cubic units.

Similar Questions

$(\overrightarrow{a}+2 \overrightarrow{b}-\overrightarrow{c}) \cdot ((\overrightarrow{a}-\overrightarrow{b}) \times (\overrightarrow{a}-\overrightarrow{b}-\overrightarrow{c}))$ is equal to

If $\vec{u}, \vec{v}, \vec{w}$ are non-coplanar vectors and $p, q$ are real numbers,then the equality $[3\vec{u}, p\vec{v}, p\vec{w}] - [p\vec{v}, \vec{w}, q\vec{u}] - [2\vec{w}, q\vec{v}, q\vec{u}] = 0$ holds for which of the following?

If $[\bar{a} \times \bar{b} \quad \bar{b} \times \bar{c} \quad \bar{c} \times \bar{a}] = \lambda [\bar{a} \quad \bar{b} \quad \bar{c}]^2$,then $\lambda$ is equal to

If $a, b, c$ are three coplanar vectors,then $[a + b, b + c, c + a] = $

If the origin and the points $(1, 2, 3)$,$(2, 3, 4)$,and $(x, y, z)$ are coplanar,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module