Three Dimensional Geometry Test

Result

Three Dimensional Geometry Test - 7

Score
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Weekly Quiz Competition

Question 1
4 / -1

The foot of the perpendicular from (2, 4, -1) to the line x + 5 = 1/4 (y + 3) = 1/9 (z - 6) is

A
(-4, 1, -3)

B
(4, -1, -3)

C
(-4, -1, 3)

D
(-4, -1, -3)
Question 2
4 / -1

A line with direction ratios proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The coordinates of each of the points of intersection are given by

A
(3a, 3a, 3a), (a, a, a)

B
(3a, 2a, 3a), (a, a, a)

C
(3a, 2a, 3a), (a, a, 2a)

D
(2a, 3a, 3a), (2a, a, a)
Question 3
4 / -1

The equation of the straight line passing through the points (4, -5, -2) and (-1, 5, 3)

A

B

C

D
Question 4
4 / -1

A
3

B
√11

C
√13

D
5
Question 5
4 / -1

A
(0, 0, 0)

B
(1, 1, 1)

C
(-1, -1, -1)

D
(1, 2, 3)

Solution
Question 6
4 / -1

If the points (1, 2, 3) and (2, -1, 0) lie on the opposite sides of the plane 2x + 3y - 2z = k, then

A
k < 1

B
k > 2

C
k < 1 or k > 2

D
1 < k < 2

Solution
Question 7
4 / -1

The volume of the tetrahedron included between the plane 3x + 4y - 5z - 60 = 0 are coordinate plane is

A
60

B
600

C
720

D
400
Question 8
4 / -1

If a plane meets the coordinate axes at A, B and C such that the centroid of the triangle is (1, 2, 4), then the equation of the plane is

A
x + 2y + 4z = 12

B
4x + 2y + z = 12

C
x + 2y + 4z = 3

D
4x + 2y + z = 3

Solution
Question 9
4 / -1

The equation of the plane through the intersection of the plane 3x - y + 2z - 4 = 0, x + y + z - 2 = 0 and the point (2, 2, 1) is

A
7x + 5y + 4z + 8 = 0

B
7x + 5y + 4z - 8 = 0

C
7x - 5y + 4z - 8 = 0

D
None of these
Question 10
4 / -1

A

B

C

D

Solution