Find the equation of the plane passing through the points (1, 1, 1) and(-2, 3, 4) and which is parrallel - Maths -

Question

Find the equation of the plane passing through the points (1, 1, 1)
and(-2, 3, 4) and which is parrallel to z axis?

Ajanta Trivedi · Accepted Answer

the equation of a plane which passes
through the point (1,1,1) is
a(x-1)+b(y-1)+c(z-1)=0  (1)
if this plane (1) also passes through the point (-2,3,4)
therefore
a(-2-1)+b(3-1)+c(4-1)=0-3a+2b+3c=0  (2)
if plane (1) is parallel to z-axis , then it's normal whose
direction ratios are a,b ,c will be perpendicular to z-axis ,
whose dc's are 0,0,1
therefore
0*a+0*b+1*c=0 (3)
now from eq(2) and eq(3), we have
a2-0=b0+3=c0-0=ka=2k and b=3ktherefore the equation of the plane is2k(x-1)+3k
(y-1)+0 (z-1)=02x-2+3y-3=02x+3y=5

hope this helps you

Find the equation of the plane passing through the points (1, 1, 1) and(-2, 3, 4) and which is parrallel to z axis?