Question

find the unit vectors perpendicular
to the plane determined by the
Points
(1,2,3), (2,-1,1),(1,2,-4).​

Answer 1

Answer:

Step-by-step explanation:Answer:

n =  

The given points are

P(1, -1, 2),  Q(2, 0, -1)  and  R(0, 2, 1)

Vector PQ = ( 2 -1 , 0 + 1 , -1 -2 ) = ( 1 , 1 , - 3 )

Vector PR = ( 0 - 2 , 2 - 0 , 1 + 1 ) = ( - 2 , 2 , 2)

Now

PQ × QR =  

PQ × QR = i (2 + 6 ) - j ( 2 - 6) + k ( 2 + 2 )

PQ × QR = 8 i + 4 j + 4 k

|PQ × QR| =  

Now

Let n be the required unit vector Perpendicular to this Plane, then

n = [PQ × QR] / |PQ × QR|

n =  

 

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