Find the equation

We know that equation of plane passing through the line of intersection of planes

(a1x + b1y + c1z + d1) + k(a2x + b2y + c2z + d2) = 0

So equation of plane passing through the line of intersection of planes

x + 2y + 3z – 4 = 0 and 2x + y – z + 5 = 0 is

x + 2y + 3z – 4 + k(2x + y – z + 5) = 0

x(1 + 2k) + y(2 + k) + z(3 – k) – 4 + 5k = 0

as given that x–intercept is twice of z intercept

so

3 – k = 2(1 + 2k)

3 – k = 2 + 4k

5k = 1

Put this value in equation (1)

x(1 + 2k) + y(2 + k) + z(3 – k) – 4 + 5k = 0

x(1 + ) + y(2 + ) + z(3 – ) – 4 + = 0

x() + y() + z() – 3 = 0

multiply by 5

7x + 11y + 14z = 15 …… (2)

And equation of the plane passing through the point is

a1(x – x1) + b1(y – y1) + c1(z – z1) = 0

and point is (2,3, – 1) so that,

a1(x – 2) + b1(y – 3) + c1(z + 1) = 0

by equation (2) a1 = 7,b1 = 11,c1 = 14

so 7(x – 2) + 11(y – 3) + 14(z + 1) = 0

7x + 11y + 14z – 14 – 33 + 14 = 0

7x + 11y + 14z – 33 = 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
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