Podcast
Questions and Answers
How many straight lines are equally inclined to the three-dimensional coordinate axes?
How many straight lines are equally inclined to the three-dimensional coordinate axes?
- 4
- 6
- 2
- 8 (correct)
Given a point P with coordinates (3, 12, 4) with respect to the origin O, what are the direction cosines of OP?
Given a point P with coordinates (3, 12, 4) with respect to the origin O, what are the direction cosines of OP?
- 3, 12, 4
- $\frac{1}{4}, \frac{1}{3}, \frac{1}{2}$
- $\frac{3}{13}, \frac{12}{13}, \frac{4}{13}$ (correct)
- $\frac{3}{\sqrt{13}}, \frac{1}{\sqrt{13}}, \frac{2}{\sqrt{13}}$
What is the projection of the line segment joining the points (-1, 0, 3) and (2, 5, 1) on the line whose direction ratios are 6, 2, 3?
What is the projection of the line segment joining the points (-1, 0, 3) and (2, 5, 1) on the line whose direction ratios are 6, 2, 3?
- $\frac{7}{22}$
- $\frac{22}{7}$
- $\frac{10}{7}$
- $\frac{18}{7}$ (correct)
The projection of a line on the coordinate axes are 3, 4, and 5 respectively. What is the length of the line?
The projection of a line on the coordinate axes are 3, 4, and 5 respectively. What is the length of the line?
If the three concurrent edges of a cube are coordinate axes, what are the direction ratios of the diagonal which joins the origin to the opposite corner?
If the three concurrent edges of a cube are coordinate axes, what are the direction ratios of the diagonal which joins the origin to the opposite corner?
A line segment has endpoints at (2, 3, 5) and (4, 7, 1). What are the direction ratios of this line segment?
A line segment has endpoints at (2, 3, 5) and (4, 7, 1). What are the direction ratios of this line segment?
Given the direction cosines of a line are proportional to 2, -1, -2, determine the actual direction cosines.
Given the direction cosines of a line are proportional to 2, -1, -2, determine the actual direction cosines.
A point P has coordinates (a, a, a) in a 3D space. What angle does the line OP make with the x-axis, where O is the origin?
A point P has coordinates (a, a, a) in a 3D space. What angle does the line OP make with the x-axis, where O is the origin?
The vertices of a triangle are A(1, 0, 0), B(0, 1, 0), and C(0, 0, 1). What is the area of triangle ABC?
The vertices of a triangle are A(1, 0, 0), B(0, 1, 0), and C(0, 0, 1). What is the area of triangle ABC?
What is the distance between point A(1,2,3) and the line passing through points B(4,5,6) and C(7,8,9)?
What is the distance between point A(1,2,3) and the line passing through points B(4,5,6) and C(7,8,9)?
Flashcards
What is 4?
What is 4?
The number of straight lines equally inclined to the three-dimensional coordinate axes.
Direction Cosines of OP?
Direction Cosines of OP?
If a point P has coordinates (3, 12, 4) with respect to origin O, the direction cosines of OP.
Formula for Projection?
Formula for Projection?
The projection of the line segment joining points (-1, 0, 3) and (2, 5, 1) on a line with direction ratios 6, 2, 3.
Line Length Formula?
Line Length Formula?
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Direction Ratios of Cube Diagonals
Direction Ratios of Cube Diagonals
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Study Notes
- The number of straight lines that are equally inclined to the three dimensional co-ordinate axes is 4.
- For point P (3, 12, 4) with respect to origin O, the direction cosines of OP are 3/√13, 12/√13, 4/√13.
- The projection of the line segment joining points (-1, 0, 3) and (2, 5, 1) on the line whose direction ratios are 6, 2, 3 is 22/7.
- Given the projection of a line on coordinate axes is 3, 4, 5, then its length is 5√2.
- The direction ratios of the diagonals of a cube which joins the origin to the opposite corner, when the 3 concurrent edges of the cube are coordinate axes, is 1, 1, 1.
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