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In this lesson, we will learn how to find the Cartesian equation of a straight line in space.

Q1:

Find the direction vector of the straight line 𝑥 − 1 6 = 𝑦 − 6 4 = 𝑧 − 8 3 .

Q2:

The straight line that passes through the point 𝐴 ( 5 , − 4 ) is perpendicular to the vector ⃑ 𝑢 = ( 5 , 2 ) . Find the Cartesian equation of the line.

Q3:

Which of the following is a Cartesian equation for a straight line that passes through the point with direction vector ?

Q4:

Find the Cartesian form of the equation of the straight line passing through the points ( − 7 , − 3 , − 7 ) and ( − 3 , − 1 0 , − 4 ) .

Q5:

What is the equation of the line parallel to line 𝑥 + 9 9 = 𝑦 + 4 1 = 𝑧 − 4 7 and passing through ( 2 , 5 , − 6 ) ?

Q6:

Find the direction vector of the straight line 𝑥 − 3 6 = 𝑦 + 2 2 = 𝑧 − 3 − 3 .

Q7:

Find the direction vector of the straight line 𝑥 − 6 − 4 = 𝑦 − 3 6 = 𝑧 − 1 7 .

Q8:

Find the direction vector of the straight line 𝑥 + 1 − 5 = 𝑦 − 4 − 2 = 𝑧 − 7 − 5 .

Q9:

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