Q. 115.0( 2 Votes )

# Find the equation of the plane through the line of intersection of the planes and and which is perpendicular to the plane ?**[CBSE 2013]**

**[CBSE 2013]**

Answer :

We know that, the equation of a plane through the line of intersection of the planes

and

is given by

So, equation of the plane passing through the line of intersection of the plane

and is given by

[] + k[] = 0

.[ + k[] – 4 + 5k = 0 …… (1)

We know that two planes perpendicular if

.

Given that plane (1) is perpendicular to the plane

Using (1)and (3) in equation (2),

[ + k()]( = 0

(1 + 2k)(5) + (2 + k)(3) + (3 – k)( – 6) = 0

5 + 10k + 6 + 3k – 18 + 6k = 0

19k – 7 = 0

k =

Put the value of k in equation (1),

.[)] – 4 + 5() = 0

.[] –

.[] –

Multiplying by 19,

Equation of required plane is,

**33x + 45y + 50z – 41 = 0**

Rate this question :

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.

Mathematics - Board PapersFind the coordinates of the point where the line through the points A (3, 4, 1) and B (5, 1, 6) crosses the XY-plane.

Mathematics - Board PapersFind the distance of the point (–1, –5, –10), from the point of intersection of the line and the plane

Mathematics - Board PapersFind the coordinates of the foot of the perpendicular and the perpendicular distance of the point P(3, 2, 1) from the plane 2x - y + z + 1 = 0. Find also, the image of the point in the plane.

Mathematics - Board PapersFind the Cartesian equation of the plane passing through the points A(0, 0, 0) and B(3, - 1, 2) and parallel to the line

Mathematics - Board PapersFind 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.

Mathematics - Board Papers