Plus Two Maths Chapter Wise Previous Questions Chapter 11 Three Dimensional Geometry are part of Plus Two Maths Chapter Wise Previous Year Questions and Answers. Here we have given Plus Two Maths Chapter Wise Previous Chapter 11 Three Dimensional Geometry.

## Kerala Plus Two Maths Chapter Wise Previous Questions and Answers Chapter 11 Three Dimensional Geometry

Question 1.

a. Find the equation of a plane which makes x, y, z intercepts respectively as 1, 2, 3.

b. Find the equation of a plane passing through the point (1,2,3) which is parallel to above plane.** [March-2018]
**Answer:

**a.**

6x+3y+2z=6

b. The normal vector for the plane is (6,3,2) The general equation of a plane is

n. (x-x_{0}, y-y_{0}, z-z_{0})=0

(6,3,2) (x-1, y-2, z-3)=0

6(x-1 )+3(y-2)+2(z-3)=0

6x+3y+2z-6-6-6=0

6x+3y+2z-18=0

6x+3y+2z =18

Question 2.

a. Find the angle between the lines

b. Find the shortest distance between the pair of lines. **[March-2018]
**

**Answer:**

**a.**

.

Question 3.

a. The line x – 1 = v = z is perpendicular to the line

a.

b. x-2=y-2=z

c.

d.

b. Find the shortest distance between the lines

Answer:

Question 4.

a. Distance of the point (0, 0, 1) from the plane x + y + z = 3.

a.

b.

c.

d.

b. 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 perpendicular to x – y + z = 0.** [March-2017]
**Answer:

a. Perpendicular distance of (0, 0, 1) from the plane x + y + z = 3 is

b. Equation of the plane through the intersection of the given plane for each value of X is

Question 5.

Find the shortest distance between the lines.

**[March-2016]
**Answer:

Question 6.

Equation of the plane with intercepts 2,3,4 on the x, y and z axis respectively is

(i) 2x+3y+4z=1

(ii) 2x+3y+4z=12

(iii) 6x+4y+3z=1

(iv)6x+4y+3z =12

b. Find the Cartesian equation of the plane passing through the points A(2,5,-3), B(-2,-3,5) and C(5,3,-3) **[March-2016]**

Answer:

(x-2) (0+10) – (y-5) (0-24)+ (z-3) (8+24)

16x- 32 + 24y- 120 + (z + 3) (32) = 0

16x-32+24y-120 + 32z+96=0

16x + 24y+ 32z-32-120+ 96 = 0

16x + 24y+32z-56 = 0

2x + 3y + 4z – 7 = 0

Question 7.

a. Write the Cartesian equation of the straight line through the point (1,2,3) and along the vector

b. Write a general point on this straight line.

c. Find the point of intersection of this straight line with the plane 2x + 3y – z + 2 = 0.

d. Find the distance from (1, 2, 3) to the plane 2x + 3y – z + 2 = 0.** [March-2015]
**Answer:

Question 8.

The foot of the perpendicular drawn from origin to a plane is (4,-2,5).

a. How far is the plane from the origin?

b. Find a unit vector perpendicular to that plane.

c. Obtain the equation of the plane in general form. **[March-2014]
**Answer:

Question 9.

Consider the lines

a. Express the equations of the lines into vector form.

b. Find the shortest distance between the lines. **[March-2013]
**Answer:

a.

b.

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