Guess Paper – 2008

Class – XII

Subject - Mathematics

1. Show that the vector i+j+k is equally inclined with the positive directions of the coordinate axes.

2. Find unit vector perpendicular to each of the vectors 2i-j+k and i+j+k.

3. Examine whether points with position vectors -2i+3j+5k,i+2j+3k,7i-k are collinear.

4. Find distance of point(2,-1,3) from the plane r.(5i+2j-7k)+12=0.

5. Find equation of plane passing through points (1,0,2),(-1,3,2),(2,1,5).

6. Find the vector equation of the plane passing through intersection of the planes r.(i+2j+3k)=4 and r.(2i+j-k)+5=0 and which is perpendicular to the plane r.(5i+3j-6k)+8=0.

7. If a,b,c are position vectors of non-collinear points A,B,C respectively in space , show that bxc+cxa+axb is perpendicular to the plane ABC.

8. Find shortest distance between the lines r=3i+8j+3k+ג (3i-j+k) and r=-3i-7j+6k+µ (-3i+2j+4k).

9. Find foot of perpendicular drawn from the point (1,3,4) on the plane r.(2i-j+k)+3=0.

10. Minimize Z=3x+5y subject to the constraints

x-4y+12≥0, 2x+3y-12≥0, x≤4, y≥2, x≥0.

11. Show that the points with position vectors a-2b+3c,-2a+3b+2c and -8a+13b are collinear.

12. Find area of triangle whose vertices are (3,-1,2),(1,-1,-3),(4,-3,1).

13.A variable plane is at a constant distance p from the origin ,cuts the coordinate axes in A,B,C.Through A,B,C planes are drawn parallel to coordinate planes . Show that the locus of their point of intersection is x^{-2} + y^{-2} + z^{-2} = p^{-2}.

14.Show that the points(0,-1,-1),(-4,4,4),(4,5,1),and (3,9,4) are coplanar also find equation of the plane.

15.Find equation of line joining (3,4,1) and point of intersection of the line r=3i+ ג (i-j) and the plane r.(3i+j)-9=0.

16.Find the distance of the point (2,3,4) from the plane 3x + 2y +2z +5=0 measured parallel to the line

( X+3)/3 = (y-2)/6=z/2

17.Kellogg is a new cereal formed by a mixture of bran and rice that contains at least