If $a, b, c$ are distinct positive numbers and vectors $a \hat{\imath} + a \hat{\jmath} + c \hat{k}$,$\hat{\imath} + \hat{k}$,and $c \hat{\imath} + c \hat{\jmath} + b \hat{k}$ lie in a plane,then
- A$c$ is $A$.$M$. of $a$ and $b$
- B$c^2 = ab$
- C$c$ is $H$.$M$. of $a$ and $b$
- D$c$ is $G$.$M$. of $a$ and $b$
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If the volume of the parallelepiped whose coterminous edges are along the vectors $\bar{a}, \bar{b}, \bar{c}$ is $12$,then the volume of the tetrahedron whose coterminous edges are $\bar{a}+\bar{b}, \bar{b}+\bar{c}$ and $\bar{c}+\bar{a}$ is
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DifficultAP EAMCET 2021
View SolutionVolume 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.
Let $a, b$ and $c$ be three vectors. Then the scalar triple product $[a, b, c]$ is equal to:
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