Q. 194.7( 3 Votes )

Find the equation

Answer :

We know that the equation of plane passing through (x1,y1,z1) is given by

a(x – x1) + b(y – y1) + c(z – z1) = 0 …… (1)


So, equation of plane passing through (3,4,1) is


a(x – 3) + b(y – 4) + c(z – 1) = 0 ……(2)


It also passes through (0,1,0)


So, equation (2) must satisfy the point (0,1,0)


a(0 – 3) + b(1 – 4) + c(0 – 1) = 0


– 3a – 3b – c = 0


3a + 3b + c = 0 ……(3)


We know that line is parallel to plane a2x + b2y + c2z + d2 = 0 if a1a2 + b1b2 + c1c2 = 0 …… (4)


So,


a×2 + b×7 + c×5 = 0


2a + 7b + 5c = 0 ……(5)


Solving equation (3) and (5) by cross multiplication we have,





a = 8k, b = – – 13k and c = 15k


Putting the value in equation (2)


8k(x – 3) – 13k(y – 4) + 15k(z – 1) = 0


8kx – 24k – 13ky + 52k + 15kz – 15k = 0


Dividing by k we have


8x – 13y + 15z + 13 = 0


Equation of required plane is 8x – 13y + 15z + 13 = 0


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Find the equationMathematics - Board Papers

Find the coordinaMathematics - Board Papers

Find the distanceMathematics - Board Papers

Find the coordinaMathematics - Board Papers

Find the CartesiaMathematics - Board Papers

Find the coordinaMathematics - Board Papers