Vector Algebra Question 310
The length of the perpendicular from the origin to the plane passing through three non-collinear points $ \mathbf{a},,\mathbf{b},,\mathbf{c} $ is
Options:
$ \frac{[\mathbf{a},\mathbf{b},\mathbf{c}]}{|\mathbf{a}\times \mathbf{b}+\mathbf{b}\times \mathbf{c}+\mathbf{c}\times \mathbf{a}|} $
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
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Answer:
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}|} $ .
BETA
