# Worksheet: Equation of a Straight Line in Space: Cartesian and Vector Forms

In this worksheet, we will practice finding the Cartesian and vector forms of the equation of a straight line in space.

Q1:

Find the direction vector of the straight line .

• A
• B
• C
• D
• E

Q2:

Find the Cartesian form of the equation of the straight line passing through the points and .

• A
• B
• C
• D

Q3:

Find the direction vector of the straight line .

• A
• B
• C
• D
• E

Q4:

Find the direction vector of the straight line .

• A
• B
• C
• D
• E

Q5:

Find the direction vector of the straight line .

• A
• B
• C
• D
• E

Q6:

Give the Cartesian equation of the line .

• A
• B
• C
• D

Q7:

Find the Cartesian form of the equation of the straight line passing through the point and makes equal angles with the coordinates axes.

• A
• B
• C
• D

Q8:

Give the Cartesian equation of the line through point and with direction vector .

• A
• B
• C
• D

Q9:

Give the vector equation of the line through the point with direction vector .

• A
• B
• C
• D

Q10:

Find the direction vector of the straight line passing through and .

• A
• B
• C
• D

Q11:

Give a direction vector of the line through the origin and the point .

• A
• B
• C
• D

Q12:

Find the direction cosines of the straight line whose direction ratio is .

• A,
• B,
• C,
• D,
• E,

Q13:

If the direction cosines of a straight line are , then find the possible values of .

• A,
• B3,
• C2,
• D,

Q14:

Give the equations for the -axis in 3-dimensional space.

• A,
• B,
• C
• D
• E

Q15:

Give equations for the -axis in 3-dimensional space.

• A,
• B
• C
• D,
• E

Q16:

Give the equations for the -axis in 3-dimensional space.

• A,
• B
• C,
• D
• E

Q17:

Find the vector form of the equation of the straight line passing through the point and the center of the sphere whose equation is .

• A
• B
• C
• D

Q18:

Determine, in vector form, the equation of the straight line that passes through the points and .

• A
• B
• C
• D

Q19:

The points , , and form a triangle. Determine, in vector form, the equation of the median drawn from .

• A
• B
• C
• D

Q20:

Find the vector form of the equation of the straight line .

• A
• B
• C
• D