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# Find the equation of the plane which contains the line of intersection of the planes r.(i−2j+3k)−4=0 and r.(-2i+j+k)+5=0 and whose intercept on x-axis is equal to that of on y-axis. - CBSE (Science) Class 12 - Mathematics

ConceptVector and Cartesian Equation of a Plane

#### Question

Find the equation of the plane which contains the line of intersection of the planes

vecr.(hati-2hatj+3hatk)-4=0" and"

vecr.(-2hati+hatj+hatk)+5=0

and whose intercept on x-axis is equal to that of on y-axis.

#### Solution

vecr.(hati-2hatj+3hatk)-4=0

vecr.(-2hati+hatj+hatk)+5=0

vecr.(hati-2hatj+3hatk)+lambda{vecr.(-2hati+hatj+hatk)}-4+5lambda = 0

=>vecr.[(1-2lambda)hati+(-2+lambda)hatj+(3+lambda)hatk]-4+5lambda=0

=>(1-2lambda)x+(-2+lambda)y+(3+lambda)z=-5lambda+4

=>x/((-5lambda+4)/(1-2lambda))+y/((-5lambda+4)/(-2+lambda))+z/((-5lambda+4)/(3+lambda))=1

:.(-5lambda+4)/(1-2lambda) =(-5lambda+4)/(-2+lambda)

⇒ 1- 2λ = -2 + λ

⇒ -3λ = -3

⇒ λ = 1

∴ Equation of the required plane

- x - y + 4z = -1

x + y - 4z - 1 = 0

Vector eqn of the required Plane

=>vecr.(hati+hatj-4hatk)-1=0

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Solution Find the equation of the plane which contains the line of intersection of the planes r.(i−2j+3k)−4=0 and r.(-2i+j+k)+5=0 and whose intercept on x-axis is equal to that of on y-axis. Concept: Vector and Cartesian Equation of a Plane.
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