Q. 334.7( 3 Votes )
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]
Answer :
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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