JEE Main Mathematics: 3D Geometry Practice Questions

11 questions with answers and step-by-step solutions. Tap any question to see the full worked solution.

Q1.
$Find the direction cosines of the vector (1, 2, 2).$
Easy
Q2.
$Find the distance between the points P(1, 2, 3) and Q(4, 6, 3).$
Easy
Q3.
$Find the midpoint of the line segment joining (2, 4, 6) and (4, 2, 0).$
Easy
Q4.
$What is the equation of the plane passing through the point (1, 1, 1) and perpendicular to the vector (1, 0, 0)?$
Easy
Q5.
$The angle between the line (x-1)/2 = (y-2)/1 = (z+3)/-2 and the plane x + y + 4z = 9 is:$
Medium
Q6.
$Find the shortest distance between the lines (x-1)/2 = (y-2)/3 = (z-3)/4 and (x-2)/3 = (y-4)/4 = (z-5)/5.$
Medium
Q7.
$The equation of the plane passing through the intersection of the planes x + y + z = 6 and 2x + 3y + 4z + 5 = 0 and the point (1, 1, 1) is:$
Medium
Q8.
$The distance of the point (1, -2, 3) from the plane passing through the points (1, 2, 3), (-1, 3, 0), and (2, 1, -1) is:$
Medium
Q9.
$Find the image of the point (1, 2, 3) in the plane x + y + z = 6.$
Hard
Q10.
$The angle between the line (x-1)/1 = (y-2)/2 = (z-3)/3 and the plane x + y + z = 0 is:$
Hard
Q11.
$Find the equation of the sphere which has its center at (1, 2, 3) and touches the plane 2x - y + 2z = 0.$
Hard

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