3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - JEE MCQ
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10 Questions MCQ Test - 3-D Geometry: Direction Ratios and Direction Cosines(13 Dec)
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3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 1
The direction cosines l, m and n of two lines are connected by the relations l + m + n = 0 and lm = 0, then the angle between the lines is
Detailed Solution for 3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 1
...(i)
or 
, then putting in equation (i), we get 
i.e. 
, then putting in equation (i), we get 
i.e.
3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 2
A line makes 
with positive 
-axis and makes equal angles with positive 
axes, respectively. What is the sum of the three angles which the line makes with positive 
and 
axes?
Detailed Solution for 3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 2
i.e. 
and 
)
, Negative value is discarded,
Required sum 
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3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 3
What are the direction cosines of a line which is equally inclined to the positive directions of the axes?
Detailed Solution for 3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 3
3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 4
A line makes the same angle 
with each of the 
and 
axes. If the angle 
, which it makes with the 
-axis, is such that 
, then what is the value of 
?
with each of the and axes. If the angle , which it makes with the -axis, is such that , then what is the value of ?
Detailed Solution for 3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 4
line makes the same angle 
with 
and 
-axes and 
with z-axis) Also, 
.......(2)
3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 5
If a line makes angle 
and 
with the 
-axis and 
-axis respectively, then the angle made by the line with the 
-axis is
Detailed Solution for 3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 5
3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 6
The direction cosines of two lines are related by l + m + n = 0 and al2 + bm2 + cn2 = 0. The lines are parallel if
Detailed Solution for 3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 6
or 
will get final answer.
3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 7
A line makes angles 
and 
with 
axes respectively. Consider the following
1.
2.
3.
Which of the above is/are correct?
and with axes respectively. Consider the following1.
2.
3.
Which of the above is/are correct?
Detailed Solution for 3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 7
and 
with 
axes respectively, then 
Statement (2) is correct.
3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 8
Consider the following relations among the angles 
and 
made by a vector with the coordinate axes
1.
II.
Which of the above is/are correct?
and made by a vector with the coordinate axes1.
II.
Which of the above is/are correct?
Detailed Solution for 3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 8
...(i)
3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 9
If the direction cosines of a line are 
then
then
Detailed Solution for 3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 9
3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 10
If a line makes angles 
with the positive directions of 
and 
-axes respectively, then the value of 
with the positive directions of and -axes respectively, then the value of
Detailed Solution for 3-D Geometry: Direction Ratios and Direction Cosines(13 Dec) - Question 10
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