Given position vectors: OA ( i + 2j - k) ; OB ( -i + 2j +3k); OC ( 2i + j + 4k)
Given that OA is perpendicular to OB.
The Question : Show that OA is normal to the plane OBC.
r . n = d
To find the normal of the plane OBC, I used n = BO x BC
d = OB . n
The Attempt at a Solution
Equation of plane OBC:
BO = -OB = i - 2j - 3k
BC = OC - OB = (2,1,4) - (-1,2,3) = (3,-1,1)
n = BO x BC = (5,10,-5)
d = OB . n = (-1,2,3) . (5,10,-5) = 0
∴ Equation of plane OBC = r. (5,10,-5) = 0
How do I show that OA is normal to the plane? I know that it is related to the statement - 'OA is perpendicular to OB'. However, I do not know how can it be applied into the question.
I hope someone can help me out.
Thank you for your time!