The volume of the tetrahedron formed by the c | vedclass

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

Question

(C) The volume of a tetrahedron with coterminous edges $\vec{a}, \vec{b}, \vec{c}$ is given by $V_{tetrahedron} = \frac{1}{6} |[\vec{a} \, \vec{b} \,

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(C) The volume of a tetrahedron with coterminous edges $\vec{a}, \vec{b}, \vec{c}$ is given by $V_{tetrahedron} = \frac{1}{6} |[\vec{a} \, \vec{b} \, \vec{c}]|$.Given $V_{tetrahedron} = 3$,we have $\frac{1}{6} |[\vec{a} \, \vec{b} \, \vec{c}]| = 3$,which implies $|[\vec{a} \, \vec{b} \, \vec{c}]| = 18$.The volume of a parallelepiped with coterminous edges $\vec{a} + \vec{b}, \vec{b} + \vec{c}, \vec{c} + \vec{a}$ is given by the scalar triple product $|[(\vec{a} + \vec{b}) \, (\vec{b} + \vec{c}) \, (\vec{c} + \vec{a})]|$.Using the property of scalar triple products,$[\vec{a} + \vec{b}, \vec{b} + \vec{c}, \vec{c} + \vec{a}] = 2[\vec{a} \, \vec{b} \, \vec{c}]$.Therefore,the volume is $2 	imes 18 = 36$.

The volume of the tetrahedron formed by the coterminous edges $\vec{a}, \vec{b}, \vec{c}$ is $3$. Then the volume of the parallelepiped formed by the coterminous edges $\vec{a} + \vec{b}, \vec{b} + \vec{c}, \vec{c} + \vec{a}$ is

Similar Questions

Which of the following species has no $p\pi - p\pi$ bond but has a bond order equal to that of $O_2$?

The locus of the centroid of the triangle with vertices at $(a \cos \theta, a \sin \theta)$,$(b \sin \theta, -b \cos \theta)$ and $(1, 0)$ is (where $\theta$ is a parameter).

The major product of the following reaction is

Vasoconstriction leads to........

The figure shows a system of logic gates. From the study of the truth table,it can be found that to produce a high output $(1)$ at $R$,we must have

Vedclass Test Series

Exam Paper Generator

Online Exam Module