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Algebra

# 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 + sin 2 γ = 3. The point at which the line joining the points (2, - 3, 1) & (3, - 4, - 5) intersects the plane, 2x + y + z = 7 is 4. All the points on the x - axis have : 5. Distance between the points (1, 3, 2) and (2, 1, 3) is : (A) 12 (B) 12 (C) 6 (D) 6 6. The direction cosines of the line, x = y = z are : 1 3 1 3 , , 1 3 1 3 , , 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 : - - 1 11 9 11 25 11 , , 8. Which of the following set of points arre non-collinear ? 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 : (A) 1 3 (B) 1 2 (C) 1 3 (D) 1 2 10. The equation of the st. line passing through (1, 2, 3) and perpendicular to the plane x + 2y - 5z = 0 is : 1 1 2 2 3 5 2 2 5 3 1 1 2 2 3 5 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) a = b = c (B) f = g = h = 0 (C) v = u = w (D) a = b = c & f = g = h = 0 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 lscript is the equation of the line through (1, 2, - 1) and (- 1, 0, 1), then ( l , m, n) is : 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 : 14. The value of k for which the planes 3x - 6y - 2z = 7 and 2x + y - kz = 5 are perpendicular to each other is : (A) 0 (B) 1 (C) 2 (D) 3 15. x + y + z + 2 = 0 together with x + y + z + 3 = 0 represents in space
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Algebra - 3 Dimensional Coordinate Geometry 1 The angle...

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