# Three Dimensional Geometry - Online Test

Q1.
Equation of a line through a point  and having direction cosines l, m, n is

Explaination / Solution:

Equation of a line through a point (x1, y1, z1) and having direction cosines l, m, n is given by :

Q2. Vector equation of a line that passes through two points whose position vectors are  is
Explaination / Solution:

Vector equation of a line that passes through two points whose position vectors are  is given by:

Q3.
Cartesian equation of a line that passes through two points and  is

Explaination / Solution:

Cartesian equation of a line that passes through two points  and is given by : .

Q4.
If  is the acute angle between , then

Explaination / Solution:

If  is the acute angle between , then cosine of the angle between these two lines is given by :

Q5. Shortest distance between two skew lines is
Explaination / Solution:

Shortest distance between two skew lines is The line segment perpendicular to both the lines .

Q6. Shortest distance between is
Explaination / Solution:

Shortest distance between
is given by :

Q7.
Shortest distance between the lines and is
Explaination / Solution:

Shortest distance between the lines and is given by:

Q8.
If a line makes angles  with the x, y and z – axes respectively, find its direction cosines.

Explaination / Solution:

If a line makes angles  with the x, y and z – axes respectively, then the direction cosines of this line is given by :

Q9. If a line has the direction ratios – 18, 12, – 4, then what are its direction cosines ?
Explaination / Solution:

If a line has the direction ratios – 18, 12, – 4, then its direction cosines are given by:

Q10.
Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector.

Explaination / Solution:

The equation of the line which passes through the point (1, 2, 3) and is parallel to the vector
, let vector  and vector
the equation of line is :
.