The ratio in which the plane r.(i-2 j+3k) = 17 divides the line joining the points...

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The ratio in which the plane r.(i-2 j+3k) = 17 divides the line joining the points -2i+4j+7k and si-5j+8k 1) 1:5 2) 1: 10 3) 3:5 4) 3: 10 If the points (1, 1, -3) and (1, 0, -3) lie on opposite sides of the plane x+y + 3z + d 0 then 1) d< 7 2) d> 8 3) 7 <d < 8 4) d< 7 or d> 8. 10 If the areas of triangles formed by a plane with the positive X, Y: Y, Z: Z,X axes respectively are 12, 9. 6 sq. unit respectively then the equation of the plane is y +ニ=1 1) 4 6 3 y X y x y, z 4)+ー+ニ=1 3 6 4 2) -+ +ニ=1 3) +ニ=1 6 3 4 3 4 6 11. The intercepts of the plane 2x -3y + 4z 12 on the coordinate axes are given by 1) 3, -2, 1.5 2) 6, -4, 3 3) 6, -4, -3 4) 2, -3, 4 12. If the plane 7x +11y + 13z 3003meets the coordinate axes in A,B,C then the centroid of the AABC is 1) (143,91,77) 2) (143,77,91) 3) (91, 143,77) 4) (143, 66, 91) 13. The length of projection of the line segment joining the points (1, 0,-1) and (-1, 2, 2) on the plane x+3y- 5z 6 is equal to 472 3) V 31 271 474 1) 2 2) 53 4) 35 14. A plane passes through (1,-2,1) and is perpendicular to two planes 2x- 2y+ z = 0 and x-y+ 2z = 4, then the distance of the plane from the point (1,2,2) is 1) 0 2) 1 3) 2 4) 2/2 15. Distance between two parallel planes 2x + y + 2z 8 and 4x + 2y + 4z + 5 = 0 is 7 3) 5 4) 9. 3 1) 2) 2 16. A plane passes through the point (1, -2, 3) and is parallel to the plane 2r 2y + z 0. The distance of the point (-1, 2, 0) from the plane is 1) 2 2) 3 3) 4 4) 5 17. The equation of the plane containing the lines 2x -5y +z = 3,r+ y+ 4z 5 and parallel to the plane x+3y + 6z 1, is 1) 2x + 6y +12z = 13 2) x +3y +6z = -7 3) x +3y +6z = 7 4) 2x +6y +12z = -13 18. An equation of a plane parallel to the plane x-2y +2z -5 0 and at a unit distance from the origin is 1) x-2y +2z -7 = 0 3) x-2y +2z-3 = 0 2) x -2y +2z +5 = 0 4) x-2y +2z +1= 0 Sri Chaitar 137 The ratio in which the plane r.(i-2 j+3k) = 17 divides the line joining the points -2i+4j+7k and si-5j+8k 1) 1:5 2) 1: 10 3) 3:5 4) 3: 10 If the points (1, 1, -3) and (1, 0, -3) lie on opposite sides of the plane x+y + 3z + d 0 then 1) d< 7 2) d> 8 3) 7 <d < 8 4) d< 7 or d> 8. 10 If the areas of triangles formed by a plane with the positive X, Y: Y, Z: Z,X axes respectively are 12, 9. 6 sq. unit respectively then the equation of the plane is y +ニ=1 1) 4 6 3 y X y x y, z 4)+ー+ニ=1 3 6 4 2) -+ +ニ=1 3) +ニ=1 6 3 4 3 4 6 11. The intercepts of the plane 2x -3y + 4z 12 on the coordinate axes are given by 1) 3, -2, 1.5 2) 6, -4, 3 3) 6, -4, -3 4) 2, -3, 4 12. If the plane 7x +11y + 13z 3003meets the coordinate axes in A,B,C then the centroid of the AABC is 1) (143,91,77) 2) (143,77,91) 3) (91, 143,77) 4) (143, 66, 91) 13. The length of projection of the line segment joining the points (1, 0,-1) and (-1, 2, 2) on the plane x+3y- 5z 6 is equal to 472 3) V 31 271 474 1) 2 2) 53 4) 35 14. A plane passes through (1,-2,1) and is perpendicular to two planes 2x- 2y+ z = 0 and x-y+ 2z = 4, then the distance of the plane from the point (1,2,2) is 1) 0 2) 1 3) 2 4) 2/2 15. Distance between two parallel planes 2x + y + 2z 8 and 4x + 2y + 4z + 5 = 0 is 7 3) 5 4) 9. 3 1) 2) 2 16. A plane passes through the point (1, -2, 3) and is parallel to the plane 2r 2y + z 0. The distance of the point (-1, 2, 0) from the plane is 1) 2 2) 3 3) 4 4) 5 17. The equation of the plane containing the lines 2x -5y +z = 3,r+ y+ 4z 5 and parallel to the plane x+3y + 6z 1, is 1) 2x + 6y +12z = 13 2) x +3y +6z = -7 3) x +3y +6z = 7 4) 2x +6y +12z = -13 18. An equation of a plane parallel to the plane x-2y +2z -5 0 and at a unit distance from the origin is 1) x-2y +2z -7 = 0 3) x-2y +2z-3 = 0 2) x -2y +2z +5 = 0 4) x-2y +2z +1= 0 Sri Chaitar 137