A) \[\frac{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}{|\mathbf{a}\times \mathbf{b}+\mathbf{c}\times \mathbf{a}+\mathbf{b}\times \mathbf{c}|}\]
B) \[\frac{2\,[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}{|\mathbf{a}\times \mathbf{b}+\mathbf{b}\times \mathbf{c}+\mathbf{c}\times \mathbf{a}|}\]
C) \[[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]\]
D) None of these
Correct Answer: A
Solution :
The vector equation of the plane passing through points \[\mathbf{a},\mathbf{b},\mathbf{c}\] is \[\mathbf{r}.(\mathbf{a}\times \mathbf{b}+\mathbf{b}\times \mathbf{c}+\mathbf{c}\times \mathbf{a})=[\mathbf{a}\ \mathbf{b}\ \mathbf{c}]\] Therefore, the length of the perpendicular from the origin to this plane is given by \[\frac{[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]}{|\mathbf{a}\times \mathbf{b}+\mathbf{b}\times \mathbf{c}+\mathbf{c}\times \mathbf{a}|}\].
You need to login to perform this action.
You will be redirected in
3 sec
