Three Dimensional Geometry Test

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Three Dimensional Geometry Test - 1

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Question 1
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Direction cosines of a line are

A
The cosines of the angles made by the line with the positive directions of the coordinate axes.

B
The sines of the angles made by the line with the positive directions of the coordinate axes.

C
The tangents of the angles made by the line with the negative directions of the coordinate axes.

D
The cotangents of the angles made by the line with the negative directions of the coordinate axes.

Solution

Explanation:

a line when intersect another line or axis two kind of angle form ,as an assumption we take positive side of axis, to define the direction of line we take angle made from all three axis.and we take cos not other trigonometric function like sin,tan because we can define Direction cosines of a line are coefficient of i,j,k of a unit vector along that line.
Question 2
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If l, m and n are the direction cosines of a line, Direction ratios of the line are the numbers which are

A
Proportional to the direction cosine l of the line

B
Inversely Proportional to the direction cosines of the line

C
Proportional to the direction cosines of the line.

D
Inversely Proportional to the direction cosine l of the line

Solution

Explanation:

If l, m and n are the direction cosines of a line, Direction ratios of the line are the numbers which are Proportional to the direction cosines of the line.
Question 3
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Skew lines are lines in different planes which are

A
parallel and intersecting

B
intersecting

C
parallel

D
neither parallel nor intersecting

Solution

Explanation:

By definition : The Skew lines are lines in different planes which are neither parallel nor intersecting .
Question 4
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Angle between skew lines is

A
the angle between two non intersecting lines drawn from any point anti – parallel to each of the skew lines

B
the angle between two intersecting lines drawn from any point perpendicular to each of the skew lines

C
the angle between two intersecting lines drawn from any point parallel to each of the skew lines

D
the angle between two non intersecting lines drawn from any point parallel to each of the skew lines

Solution

Explanation:

Angle between skew lines is the angle between two intersecting lines drawn from any point parallel to each of the skew lines .