# Find the vector equation of the line passing through (1, 2, 3) and parallel to each of the planes and . Also, find the point of intersection of the line thus obtained with the plane .[CBSE 2018]

Given: Line is parallel to two planes  and

Equation of required line is –(i)

Now, any point on line (i) is

For this line to intersect the plane

We have, (1–3λ)2 + (2 + 5λ)1 + (3 + 4λ)1 = 4

λ = –1

Point of intersection is (4,–3,–1)

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