Three Dimensional Geometry - Online Test
Q1. The equation of a plane through a point whose position vector is and perpendicular to the vector . is
Answer : Option C
Explaination / Solution:
In vector form The equation of a plane through a point whose position vector is and perpendicular to the vector . Is given by :
Q2. Equation of a plane passing through three non collinear points (x1, y1, z1),(x2, y2, z2) and (x3, y3, z3) is
Answer : Option D
Explaination / Solution:
In cartesian co – ordinate system : Equation of a plane passing through three non collinear points (x1, y1, z1),(x2, y2, z2) and (x3, y3, z3) is given by : 
Q3. Vector equation of a plane that contains three non collinear points having position vectors 
is
is
Answer : Option D
Explaination / Solution:
Vector equation of a plane that contains three non collinear points having position vectors 
is given by: 
is given by:
Q4. Equation of a plane that cuts the coordinates axes at (a, 0, 0), (0, b, 0) and (0, 0, c) is
Answer : Option D
Explaination / Solution:
Equation of a plane that cuts the coordinates axes at (a, 0, 0), (0, b, 0) and (0, 0, c) is called the equation of plane in intercept form having intercepts a , b , and c on coordinate axis i.e. at x- axis , y – axis and z – axis respectively is given by : .
Q5. Vector equation of a plane that passes through the intersection of planes 
expressed in terms of a non – zero constant is
expressed in terms of a non – zero constant is
Answer : Option C
Explaination / Solution:
Vector equation of a plane that passes through the intersection of planes 
expressed in terms of a non – zero constant is given by: 
expressed in terms of a non – zero constant is given by:
Q6. Two lines 
are coplanar if
are coplanar if
Answer : Option D
Explaination / Solution:
In vector form:
Two lines 
are coplanar if (
.
are coplanar if (
Q7. In the Cartesian form two linesand are coplanar if
Answer : Option D
Explaination / Solution:
In the Cartesian form two linesand are coplanar if
Q8. In vector form, if is the angle between the two planes 
then
then
Answer : Option B
Explaination / Solution:
In vector form, if is the angle between the two planes 
then, cosine of the angle between these two lines is given by : 
then, cosine of the angle between these two lines is given by :
Q9. Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x – y + z = 0.
Answer : Option D
Explaination / Solution:
The equation of the plane through the line of intersection of the planes
Q10. Find the angle between the planes whose vector equations are 
Answer : Option A
Explaination / Solution:
