Algebra - 3- Dimensional Coordinate Geometry 1. The angle...

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1 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 1. The angle between the planes, 3x - 4y + 5z = 0 & 2x - y - 2z = 5, is (A) π 3 (B) π 2 (C) π 6 (D) None of these 2. If α , β , γ be the angles which a line makes with the co-ordinate axes, then sin 2 α + sin 2 β 2 γ = 2 1 3 3. The point at which the line joining the points (2, - 3, 1) & (3, - 4, - 5) intersects the plane, 2x + y + z = 7 is (1, 2, 7) (1, - 2, 7) (- 1, 2, 7) 2, - 7) 4. All the points on the x - axis have : x = 0 y = 0 x = 0, y = 0 y = 0, x = 0 5. Distance between the points (1, 3, 2) and (2, 1, 3) is : 12 12 6 6 6. The direction cosines of the line, x = y = z are : (A) 1 3 1 3 1 3 , , 1 3 1 3 1 3 , , 5 13 10 , , (D) 1 13 1 10 1 5 , , 7. The point of intersection of the line x y z 1 1 2 2 3 = - = + and the plane, 2x + 3y + z = 0, is : (0, 1, - 2) (1, 2, 3) ( - 1, 9, - 25) - - 1 11 9 11 25 11 , , 8. Which of the following set of points arre non-collinear ? 1, 1), (- 1, 1, 1), (0, 0, 1) (1, 2, 3), (3, 2, 1), (2, 2, 2) ( - 2, 4, - 3), (4, - 3, - 2), ( - - 4) (2, 0, - 1), (3, 2, - 2), (5, 6, - 4) 9. If a straight line in space is equally inclined to the co-ordinate axes, the cosine of the angle of inclination to any one of the axes is : 1 3 1 2 1 3 1 2 10. The equation of the st. line passing through (1, 2, 3) and perpendicular to the plane x + 2y - 5z = 0 is : x y z - = - = - - 1 1 2 2 3 5 x y z - = - = + 1 1 2 2 5 3 x y z + = + = + - 1 1 2 2 3 5 x y z + = + = - 1 1 2 2 5 3 11. Equation, ax 2 + by 2 + cz 2 + 2 fyz + 2 gzx + 2 hxy + 2 ux + 2 vy + 2 wz + d = 0 represents a sphere, if : a = b = c f = g = h = 0 v = u = w a = b = c 3- Dimensional Coordinate Geometry
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2 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 12. If, x y m z n - = - = + 1 2 1 l is the equation of the line through (1, 2, - 1) and (- 1, 0, 1), then ( l , m, n) is : (A) 1, 0, 1) (B) (1, 1, - 1) (C) (1, 2, - 1) (D) (0, 1, 0) 13. A point moves so that the sum of its distances from the points (4, 0, 0) and 4, 0, 0) remains 10 . The locus of the point is : 9 x 2 - 25 y 2 + 25 z 2 = 225 9 x 2 y 2 z 2 9 x 2 y 2 z 2 9 x 2 y 2 z 2 + 225 = 0 14. The value of k for which the planes 3x - 6y - 2z = 7 and 2x + y - kz = 5 are perpendicular to each other is : 0 1 2 3 15. x + y + z + 2 = 0 together with x + y + z + 3 = 0 represents in space A line A point A plane None of these 16. The distance between the planes, x + 2y + 3z + 7 = 0 & 2x + 4y + 6z + 7 = 0 is : 7 2 2 7 2 7 2 7 2 2 17. The equation of the plane through (1, 2, 3) and parallel to the plane 2x + 3y - 4z is : 2x + 3y + 4z = 4 2x + 3y + 4z + 4 = 0 2x - 3y + 4z + 4 = 0 2x + 3y - 4z + 4 = 0 18. Distance of the point (2, 3, 4) from the plane, 3x - 6y + 2z + 11 = 0 is 1 2 3 0 19. The point of intersection of lines, x y z - = - = 4 5 1 2 1 & x y z - = - = - 1 2 2 3 3 4 (A) ( - 1, - - 1) (B) ( - 1, - 1, 1) (C) (1, - - 1) ( - 1, 1, - 1) 20. If 4x + 4y + kz = 0 is the equation of the plane through the origin that contains the line, x y z - = + = 1 2 1 3 4 , then k = 1 3 5 7 21. xy - plane divides the line joining the points (2, 4, 5) and (- 4, 3, - 2) in the ratio : 3 : 5 5 : 2 1 : 3 3 : 4 22.
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Algebra - 3- Dimensional Coordinate Geometry 1. The angle...

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