Q10 of 181 Page 1205

Find the vector equation of the plane passing through the intersection of the planes and and passing through the point (-2, 1, 3).

Equation of plane through the line of intersection of two planes in vector form is

(1)


Where the standard equation of planes are



Putting values in equation(1)



(2)


Now as the plane passes through (-2,1,3)



Putting in equation (2)



-2.(2 + 3λ) + 1.(-7-5λ) + 3.(4 + 4λ)=3-11λ


-4-6λ-7-5λ + 12 + 12λ-3 + 11λ=0


-14 + 12 + 12λ=0



Putting the value of λ in equation (2)






More from this chapter

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8

Find the vector equation of the plane through the intersection of the planes and and passing through the point (2, 1, -1).

 9

Find the vector equation of the plane through the point (1, 1, 1), and passing through the intersection of the planes and

11

Find the equation of the plane through the line of intersection of the planes and and perpendicular to the plane

12

Find the Cartesian and vector equations of the planes through the line of intersection of the planes and which are at a unit distance from the origin.