Q30 of 34 Page 11

Find the equation of the plane containing two parallel lines and Also, find if the plane thus obtained contains the line or not. [CBSE 2016]

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.

More from this chapter

All 34 →
28

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]

 29

Find the position vector of the foot of perpendicular and the perpendicular distance from the point P with position vector to the plane Also find image of P in the plane.[CBSE 2016]

 31

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is [CBSE 2017]

 32

Find the coordinates of the point where the line through the points (3, -4, -5) and (2, -3, 1), crosses the plane determined by the points (1,2,3), (4,2, -3) and (0,4, 3).[CBSE 2017]