Q. 184.5( 2 Votes )

# Find the equation of plane passing through the points A (3, 2, 1), B (4, 2, - 2) and C(6, 5, - 1) and hence find the value of for which A (3, 2, 1), B(4, 2, - 2), C(6, 5, - 1) and are coplanar

**OR**

Find the co - ordinates of the point where the line meets the plane which is perpendicular to the vector and at a distance of from origin**[CBSE 2016]**

**[CBSE 2016]**

Answer :

**Given:** A (3, 2, 1) B (4, 2, - 2) C (6, 5, - 1)

**Formula:** equation of plane is given by

Substituting the values in above equation

(x - 3)9 – (y - 2)7 + (z - 1)3 = 0

9x - 7y + 3z = 16

Now if A, B, C, and D are co - planar D must lie on the plane

9λ - 35 + 15 - 16 = 0

λ = 4

**OR**

**given:**

Equation of plane perpendicular to at a distance of from origin is

= (-1 + 3λ)1 + (-2 + 4λ)1 + (-3 + 3λ)3 = 4

16λ = 16

λ = 1

Hence substituting λ = 1 in

The point of intersection is ( - 1 + 3, - 2 + 2, - 3 + 3) which is

(2, 2, 0)

Rate this question :

Find the equation of the line passing through the point (–1, 3, –2) and perpendicular to the lines and

Mathematics - Board PapersFind the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x - y + z = 0. Also find the distance of the plane obtained above, from the origin.

**OR**

Find the distance of the point (2, 12, 5) from the point of intersection of the line and the plane

Mathematics - Board PapersFind the length of the perpendicular drawn from the origin to the plane 2x – 3y + 6z + 21 = 0.

Mathematics - Board PapersFind the coordinates of the foot of perpendicular and the length of the perpendicular drawn from the point P (5, 4, 2) to the line . Also find the image of P in this line.

Mathematics - Board PapersShow that the lines and intersect. Find their point of intersection.

Mathematics - Board Papers