CBSE Class 12 Mathematics Important Questions Chapter 11 – Three Dimensional Geometry
23. Find x such that four points A(3,2,1) B(4,x,5)(4,2,-2) and D (6,5,-1)are coplanar.
Ans: The equation of plane through
A(3,2,1), C(4,2,-2) and D (6,5,-1) is
The point A,B,C,D are coplanar
24. Find the angle between the two planes 2x +y-2z=5 and 3x -6y -2z = 7using vector method.
Ans.
25. Find the angle b/w the line
Ans:
6 Marks Questions
1.Find the vector equation of the plane passing through the intersection of plane And the point (1,1,1)
Ans.
Using the relation
2. Find the coordinate where the line thorough (3,-4,-5) and ((2,-3,1) crosses the plane 2x + y + z = 7
Ans. Given points are A(3,-4,-5)
B(2,-3,1)
Direction ration of AB are 3-2, -4+3, -5-1
1,-1,-6
Eq. of line AB
are the required point
3. Find the equation of the plane through the intersection of the planes
3x – y + 2z -4 = 0 and x + y + z – 2 = 0 and the point (2,2,1)
Ans. Equation of any plane through the
intersection of given planes can be taken as
The point (2,2,1) lies in this plane
put in eq ….(i)
4. If the points (1,1p) and (-3,0,1)be equidistant from the plane , then find the value of p.
Ans.The given plane is
This plane is equidistant from the points (1,1,P) and (-3,0,1)
5. Find the equation of the plane through the line of intersection of the planes
x +y +z = 1 and 2x + 3y + 4z = 5 which is of the plane x-y + z = 0
Ans. Equations of any plane through the intersection of given planes are be written is
This plane is it right angle to the plane x-y+z
6. Find the distance of the point (-1,-5,-10) from the point of intersection of the line and the plane
Ans
Are the coordinate of the point of intersection of the given line and the plane
7. Find the equation of the plane that contains the point (1,-1,2) and is to each of the plane 2x+3y-2z=5 and x+2y-3z = 8
Ans. The equation of the plane containing the given point is
A(x-1)+B(y-2)+C(Z-3)= 0….[i]
Condition of to the plane given in (i) with the plane
2x+3y-2z=5, x+2y-3z=8
2A+3B-2C=0
A+2B-3C=0
On solving
A=-5c, B=4C
5x-4y-Z=7
8. Find the vector equation of the line passing through (1,2,3) and to the planes
Ans.
9. Find the equation of the s point where the line through the points A(3,4,1) and B(5,1,6) crosses the XY plane.
Ans. The vector equation of the line through the point A and B is
Let P be the point where the line AB crosses the XY plane. Then the position vector of the point P is the form
10. Prove that if a plane has the intercepts a,b,c is at a distance of p units from the origin then
Ans. The equation of the plane in the
intercepts from is distance of
this plane from the origin is given to be p