Find the equation of the plane which contains the line of intersection of the planesandand whose intercept on the x-axis is equal to that of on y-axis.

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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Find the coordinate of the point P where the line through and crosses the plane passing through three points and Also, find the ratio in which P divides the line segment AB.

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