Prove-that-the-length-of-the-perpendicular-from-the-origin-to-the-plane-passing-through-point-a-and-containing-the-line-r-b-c-is-a-b-c-b-c-c-a-Here-a

Question Number 45856 by rahul 19 last updated on 17/Oct/18

P r o v e t h a t t h e l e n g t h o f t h e p e r p e n d i c u l a r

f r o m t h e o r i g i n t o t h e p l a n e p a s s i n g

t h r o u g h p o i n t \vec{a} a n d c o n t a i n i n g t h e

l i n e \vec{r} = \vec{b} + λ \vec{c} i s \frac{[\vec{a} \vec{b} \vec{c}]}{∣ \vec{b} \times \vec{c} + \vec{c} \times \vec{a} ∣} .

H e r e [\vec{a} \vec{b} \vec{c}] = s c a l a r t r i p l e p r o d u c t .

Commented by rahul 19 last updated on 17/Oct/18

I^{'} v e g o t e q u a t i o n o f p l a n e a s :

\vec{r} . (\vec{b} \times \vec{c} + \vec{c} \times \vec{a}) = [\vec{a} \vec{b} \vec{c}] \dots .