find the plane through (3,-3,1)and normal to the join of (3,4,-1) , (2,-1,5)
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normal vector is =(3-2)i +(4+1) j+(-1-5) k
=i +5j -6k
or,
=(2-3) i +(-1-4) j+(5+1) k
=-i -5j +6k
now equation of plane
1. (x-3)+5 (y+3)-6 (z-1)=0
x-3+5y+15 -6z+1=0
x+5y-6z+13=0
in the same way ,
-x-5y+6z-13=0
=i +5j -6k
or,
=(2-3) i +(-1-4) j+(5+1) k
=-i -5j +6k
now equation of plane
1. (x-3)+5 (y+3)-6 (z-1)=0
x-3+5y+15 -6z+1=0
x+5y-6z+13=0
in the same way ,
-x-5y+6z-13=0
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