Q28 of 34 Page 11

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

and



and whose intercept on the x-axis is equal to that of on y-axis.[CBSE 2016]

r.(i - 2j + 3k) - 4 = 0


r.( - 2i + j + k) + 5 = 0


r.(i - 2j + 3k) + λ{r.( - 2i + j + k)} - 4 + 5λ = 0


⇒ r.[(1 - 2λ)i + ( - 2 + λ)j + (3 + λ)k] - 4 + 5λ = 0


⇒ (1 - 2λ)i + ( - 2 + λ)j + (3 + λ)k = - 5λ + 4


⇒


∴


⇒ 1 - 2λ = - 2 + λ


⇒ - 3λ = - 3


⇒ λ = 1


∴ Equation of the required plane


- x - y + 4z = - 1


X + y - 4z - 1 = 0


Vector equation of the required Plane


⇒ r.(i + j - 4k) - 1 = 0

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