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In this lesson, we will learn how to find the direction vector and the equation of a straight line in three dimensions.

Q1:

Suppose that lines β π = ( 5 , β 3 , 4 ) + π‘ ( β 3 , β 1 , π ) and π₯ β 5 β = π¦ β 4 β 4 = π§ β 2 4 are parallel, what are π and β ?

Q2:

For what values of π is the line πΏ βΆ π₯ β 8 2 = π¦ β 1 0 5 = π§ + 1 3 1 parallel to the line πΏ βΆ π₯ β 2 1 0 = π¦ β 2 π + 2 = π§ β 6 1 5 2 ?

Q3:

Give the Cartesian equation of the line through point ( β 2 , 5 , 2 ) and with direction vector ( 3 , β 5 , β 4 ) .

Q4:

Find the Cartesian form of the equation of the straight line passing through the point ( β 4 , 1 , 2 ) and makes equal angles with the coordinates axes.

Q5:

Given that the lines π₯ β 8 3 = π¦ + 4 5 = π§ + 6 β 2 and π₯ β 1 0 β 5 = π¦ + 7 9 = π§ β 3 π are perpendicular, what is π ?

Q6:

Given that the vector β π΄ = ( 2 , π , 6 ) is parallel to the line π₯ β 6 3 = π¦ β 5 6 = π§ + 4 9 , find π .

Q7:

Given that πΏ βΆ π₯ + 9 β 7 = π¦ β 3 7 = π§ + 8 6 1 is perpendicular to πΏ βΆ π₯ β 2 β 9 = π¦ β 1 0 π = π§ + 3 π 2 , what is 7 π + 6 π ?

Q8:

Give the parametric equation of the line through the origin with direction vector ( 5 , β 1 , 4 ) .

Q9:

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

Q10:

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

Q11:

Which of the following is a directional vector for a line perpendicular to the -axis?

Q12:

Find the parametric equations of the straight line that passes through the point π΄ ( β 1 , 4 , β 1 ) and that is parallel to the bisector of the second quadrant of the plane π¦ π§ .

Q13:

Write the equation of the straight line πΏ passing through the points π = ( 1 , β 2 , β 3 ) 1 and π = ( 3 , 5 , 5 ) 2 in parametric form.

Q14:

Which of the following is a direction vector of the straight line π π₯ + π π¦ + π = 0 ?

Q15:

Find the equation of the line through the origin that intersects the line β π = ( β 1 , 2 , 3 ) + π‘ ( 3 , β 5 , 1 ) 1 1 orthogonally.

Q16:

Give the vector equation of the line through the point ( 3 , 7 , β 7 ) with direction vector ( 0 , β 5 , 7 ) .

Q17:

Find the direction vector of the straight line passing through π΄ ( 1 , β 2 , 7 ) and π΅ ( 4 , β 1 , 3 ) .

Q18:

Give a direction vector of the line through the origin and the point ( 6 , 6 , 1 ) .

Q19:

For what value of π do the lines π₯ β 5 = π¦ β 2 β 1 = π§ β 2 and π₯ β 1 π = π¦ + 2 4 = π§ + 1 4 intersect?

Q20:

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

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