Chapter (3 & 4)
Section (A) ( Each questions carries 1 marks)
1. The radius of the sphere 𝑥 2 + 𝑦 2 +𝑧 2 -2x +4y-8z = - 12 is
A. √2
B. 2
C. √3
1
2. If the equation of the sphere is
D. 3
1
1
3
(𝑥 − 2)2 + (𝑦 − 2)2 +(𝑧 − 2)2= 4 and one
extremity of its diameter is ( 1,0,0) , then the other extremity of the diameter of
the sphere will be
A. ( 0,1,0)
B.(0,0,1)
C.(0,1,1)
D.(1,1,1)
3. If the coordinates of the points A,B, C ,D are ( 0,0,1), ( 3,6,4), ( 0,3,1) and ( 3,0,4)
respectively, the lines AB and CD are.
A. parallel
B. skew
C. intersect D. perpendicular.
4. If the line passes through the origin and is perpendicular to the plane
3x+4y-6z+1=0, the point of intersection is
3 4 6
3
4 6
3
4 6
3 4 6
A. ( - 61 , 61,61)
B. ( -61 , − 61,61)
C. ( - 61 , − 61,61)
D. ( 61 , 61,61)
5. The point of intersection of the lines
1
1
2
A. ( 3 , − 3,− 3)
1
1
3
𝑥+1
B. ( 2 , − 2,- 2)
3
=
𝑦+3
5
=
𝑧+5
7
and
𝑥−2
1 11
1
=
𝑦−4
=
𝑧−6
3
5
1 11
is
C. ( 2 , 2,2) D. ( 3 , 3,3)
Section (B) ( Each questions carries 2 marks)
6. If the line drawn from the point(-2,-1,-3) meets a plane at a right angle at the
point ( 1,-3,3) , find the equation of the plane.
7. Find the equation of the sphere with the center at ( 2,6,-3) and radius 2.
8. Determine whether the sphere with center ( 2,4,3) and radius 4 intersects xyplane or yz-plane or zx-phane.
Section (C) ( Each questions carries 3 marks)
9. Find the Cartesian equation of the plane containing points A(0,1,2) , B( 2,3,1)
and C(-1,2,3).
10. Find the equation of the line that pass through the point (3,-2,-2) and
perpendicular to the plane -2x+3y-z= 4. Find the point of intersection of the line
and the given plane.
11. Find the equation of the plane containing the point (1,2,3) and parallel to the
plane x + y + z = 0.
Section ( D) ( Each questions carries 5 marks)
12. What is the equation of the sphere which passes through the points ( 3,0,2),
( -1,1,1) and ( 2,-5,4) and whose center lies on the plane 2x+3y+4z = 6?
13. Point A has coordinates (5,2,2) and the line ℓ passes through the points ( 2,5,-1)
and ( 1,9,-3). Point B lies on ℓ such that line AB is perpendicular to ℓ. Find the
distance between points A and B.
0
