Three Dimensional Geometry Test

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Three Dimensional Geometry Test - 3

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Question 1
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Direction cosines of a line are

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

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

Solution

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
Inversely Proportional to the direction cosines of the line

B
Inversely Proportional to the direction cosine l of the line

C
Proportional to the direction cosine l of the line

D
Proportional to the direction cosines of the line

Solution

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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Define Skew lines in a three dimensional space

A
intersecting

B
neither parallel nor intersecting

C
parallel and intersecting

D
parallel

Solution

Two lines are said to be skew lines if they are neither parallel nor intersecting.this implies two lines are skew if they are not coplanner.
Question 4
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How do we measure the angle between skew lines ?

A
The angle between any two lines parallel to the given skew lines and passing through a common point in space

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

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

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

Solution

Angle between skew lines is the angle between two lines which are parallel to the given skew lines and passing through a common point in space.