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## Homework Statement

Given position vectors: OA (

**i**+ 2

**j**-

**k**) ; OB ( -

**i**+ 2

**j**+3

**k**); OC ( 2

**i**+

**j**+ 4

**k**)

Given that OA is perpendicular to OB.

The Question : Show that OA is normal to the plane OBC.

## Homework Equations

**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**- 2

**j**- 3

**k**

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!