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Question

Find equation of the plane passing through the points P(1,1,1),Q(3,1,2),R(3,5,4) ?

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Solution

We know that,
Equation of plane passing through three non collinear,
Point...(x1,y1,z1)(x2y2,z2)(x3,y3,z3) is
∣ ∣xx1yy1zz1x2x1y3y1z2z1x3x1y3y1z3z1∣ ∣

Here,given points are P(1,1,1)Q(3,1,2)R(3,5,4)
So equation of plane is

∣ ∣x1y1z13111211315141∣ ∣=0∣ ∣x1y1z1221445∣ ∣=0

(x1)(104)(y1)(10+4)+(z+1)(88)=0(x1)6(y1)(6)+(z+1)0=0(x1)6(y1)(6)=06|(x1)+(y1)|=0(x1)+(y1)=0x+y=2


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