Q. 245.0( 2 Votes )

# Find the equation

Answer :

Given:  Taking points lying on each of the line a1 = (1, - 1, 0) and a2 = (0, 2, - 1)

Direction ratio of l1 is Let the equation of plane through a1 be

a(x - 1) + b(y + 1) + c(z) = 0 …(i) where a, b and c are the direction ratio’s

(0, 2, - 1) lies on it, therefore - a + 3b - c = 0 …(ii)

Line in eq(i) is perpendicular to the line with direction ratio’s 2, - 1, 3

Therefore, 2a - b + 3c = 0 …(iii)

Solving (ii) and (iii), by cross-multiplication, we get, Therefore, the equation of plane is

8(x - 1) + (y + 1) - 5z = 0

8x + y - 5z = 7 Point (2, 1, 2) lies on the line l3

Satisfying this point in the equation of plane to check whether l3 is contained in the plane

8(2) + 1 - 5(2) - 7 = 0

Therefore, the plane contains the given line.

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