Three Dimensional Geometry Test

Result

Three Dimensional Geometry Test - 19

Score
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Weekly Quiz Competition

Question 1
4 / -1

If direction cosines of two lines are proportional to (2, 3, -6) and (3, -4, 5), then the angle between them is

A
cos^-1 (49/36)

B
cos^-1(18√2/35)

C
96^o

D
cos^-1 (18/35)
Question 2
4 / -1

If the direction cosines of two lines are such that l + m + n = 0, l² + m² - n² = 0, then the angle between then is

A
π

B
π/3

C
π/4

D
π6
Question 3
4 / -1

The ratio in which the line joining (2, 4, 5) , (3, 5, -4) is divided by the YZ-plane, is

A
2 : 3

B
3 : 2

C
-2 : 3

D
4 : -3
Question 4
4 / -1

The cosines of ∠A of the triangle with vertices A(1, -1, 2), B(6, 11, 2) and C(1, 2, 6) is

A
63/65

B
36/65

C
16/65

D
13/64
Question 5
4 / -1

If P = (0, 1, 2), Q = (4, -2, 1) and O = (0, 0, 0), then ∠POQ is equal to

A
π/6

B
π/4

C
π/3

D
π/2
Question 6
4 / -1

If OA is equally inclined to OX, OY and OZ and if A is √3 units from the origin, then A is

A
(3, 3, 3)

B
(-1, 1, -1)

C
(-1, 1,1)

D
(1, 1, 1)

Solution
Question 7
4 / -1

A point on X-axis which equidistant from both the points (1, 2, 3) and (3, 5, -2) is

A
(-6, 0, 0)

B
(5, 0, 0)

C
(-5, 0, 0)

D
(6, 0, 0)
Question 8
4 / -1

Let O be the origin and P be the point at a distance 3 units from origin. If direction ratios of OP are (1, -2, -2), then coordinates of P is given by

A
(1, -2, -2)

B
(3, -6, -6)

C
(1/3, -2/3, -2/3)

D
(1/9, -2/9, -2/9)
Question 9
4 / -1

The direction cosines of the line passing through P(2, 3, -1) and the origin are

A

B

C

D
Question 10
4 / -1

A

B

C

D