Three Dimensional Geometry Test

Result

Three Dimensional Geometry Test - 30

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Question 1
4 / -1

The co-ordinates of the point P are (x, y, z) and the direction cosines of the line OP when O is the origin, are l, m, n. If OP = r, then

A
l = x, m = y, n = z

B
l = xr, m = yr, n = zr

C
x = lr, y = mr, z = nr

D
None of these
Question 2
4 / -1

A line makes angles α, β, γ with the co-ordinate axis. If α + β = 90°, then γ =

A
0

B
90°

C
180°

D
None of these

Solution
Question 3
4 / -1

Points (–2, 4, 7), (3, – 6, – 8) and (1, – 2, – 2) are

A
Collinear

B
Vertices of an equilateral triangle

C
Vertices of an isosceles triangle

D
None of the above

Solution
Question 4
4 / -1

A

B
1

C

D

Solution
Question 5
4 / -1

A line AB in three-dimensional space makes angle 45° and 120° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive respectively. If AB makes an acute angle θ with the positive z-axis, then θ equals

A
30°

B
45°

C
60°

D
75°

Solution
Question 6
4 / -1

If projection of any line on co-ordinate axis 3, 4, and 5, then its length is

A
12

B
50

C

D

Solution
Question 7
4 / -1

A

B

C

D

Solution
Question 8
4 / -1

The direction ratios of the line joining the points (4, 3, – 5) and (–2, 1, – 8) are

A

B
6, 2, 3

C
2, 4, –13

D
None of these

Solution
Question 9
4 / -1

The co-ordinates of the point in which the line joining the points (3, 5, – 7) and (–2, 1, 8) is intersected by the plane yz are given by

A

B

C

D

Solution
Question 10
4 / -1

The direction cosines of the line which is perpendicular to the lines whose direction cosines are proportional to (1, –1, 2) and (2, 1, –1) are

A

B

C

D

Solution