JEE Advanced Mathematics: 3D Geometry Practice Questions
11 questions with answers and step-by-step solutions. Tap any question to see the full worked solution.
- Q1.What is the equation of the plane passing through the point (1, 1, 1) and perpendicular to the vector (1, 1, 1)?Easy
- Q2.Find the direction cosines of the vector (1, 0, 0).Easy
- Q3.Find the distance between the points P(1, 2, 3) and Q(3, 4, 5).Easy
- Q4.Find the midpoint of the line segment joining (2, 4, 6) and (4, 6, 8).Easy
- Q5.What is the dot product of vectors (1, 2, 3) and (3, 2, 1)?Easy
- Q6.A plane passes through the point (1, 1, 1) and is perpendicular to the planes x + 2y + 3z = 0 and 3x + 2y + z = 0. Find the equation of the plane.Medium
- Q7.Find the shortest distance between the lines given by (x-1)/2 = (y-2)/3 = (z-3)/4 and (x-2)/3 = (y-4)/4 = (z-5)/5.Medium
- Q8.The equation of the sphere passing through the origin and the points (1, 0, 0), (0, 1, 0), and (0, 0, 1) is:Medium
- Q9.Find the projection of the line (x-1)/2 = (y+1)/-1 = (z-3)/4 on the plane x + y + z = 7.Hard
- Q10.A plane passes through the point (1, 1, 1) and is parallel to the vectors (1, 0, 2) and (0, 1, 1). Find the equation of the plane.Hard
- Q11.Consider a sphere S passing through the origin and the points (1, 0, 0), (0, 1, 0), and (0, 0, 1). Find the radius of the sphere.Hard
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