Revision Quiz on 3-D Geometry for JEE & BITSAT Exams

Question 1

If a particle A is moving also a straight line with velocity 3 m/s and another particle B has a velocity 5 m/s at an angle of 60⁰ to the path of A, then the velocity B relative to A is

Question 2

Distance between the line

and x+y-z+4=0 is

Question 3

The equation of a line and a plane is as given below. Let the angle between the line and the plane be F. What is the value of 13sin F?
L1:
P1: 3x+2y+4z+9=0

Question 4

The equation of the plane passing through the point (-1, 3, 2) and perpendicular to each of the planes x + 2y + 3z = 5 and 3x + 3y + z = 0, is

Question 5

If the angle between the given 2 planes is F. find 8sinF
P1:3x+4y+6z+9=0
P2:5x+2y+7z+8=0

Question 6

The line joining origin to the points of intersection curves ax² + 2hxy + by² + 2gx = 0 and a₁x² + 2h₁xy + b₁y² + 2g₁x = 0 will be mutually perpendicular if

Question 7

A particle has two velocities of equal magnitude inclined to each other at an angle θ. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then θ is

Question 8

The two lines x = ay + b, z = cy + d and x = a′y + b′, z = c′y + d′ will be perpendicular, if and only if

Question 9

The distance between the line

= 2

–2

+3

+ λ(

–

+4

) and the plane

.(

+5

+

) = 5 is

Question 10

if lines (x – 1)/2 = (y + 1)/3 = (z - 1)/4 and (x – 3)/1 = (y – k)/2 = z/1 intersect then what is the value of k?

Question 11

Find the equation of the line which is parallel to the line passing through the points (7,7,8) and (10,10,5) and passing through the point (1,0,5)

Question 12

A line is formed with by joining the two points as given the angles with x , y and z-axis be a, b, c.
Find (9 cos a-2 cos c)/11
The points are (14,11,19) and (11,11,11)