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

Q1:

Which of the following can be the vector form of the equation of the straight line 𝑎 𝑥 + 𝑏 𝑦 + 𝑐 = 0 , where 𝑎 ≠ 0 and 𝑏 ≠ 0 ?

Q2:

Which of the following can be the vector form of the equation of the straight line 𝑥 𝑎 + 𝑦 𝑏 = 1 , where 𝑎 ≠ 0 and 𝑏 ≠ 0 ?

Q3:

Find the vector equation of the straight line passing through the origin and the point ( 0 , 4 ) .

Q4:

Find the vector equation of the straight line passing through the points ( 6 , − 7 ) and ( − 4 , 6 ) .

Q5:

Find the vector equation of the straight line whose slope is − 8 3 and passes through the point ( 4 , − 9 ) .

Q6:

Consider the line through the point ( 3 , 6 ) and perpendicular to vector ⃑ 𝑟 = ( 3 , 6 ) . Which of the following is a vector equation of this line?

Q7:

Find the vector form of the equation of the straight line passing throught the point 𝐴 ( 2 , 5 , 5 ) and parallel to the straight line passing through the two points 𝐵 ( − 3 , − 2 , − 6 ) and 𝐶 ( 5 , 0 , − 9 ) .

Q8:

Write the vector equation of the straight line that passes through the point ( − 6 , − 9 ) with direction vector ( 9 , − 2 ) .

Q9:

Find the vector form of the equation of the straight line passing through the point ( − 5 , 1 , 4 ) and the intersection point of the two straight lines 𝑥 + 2 − 2 = 𝑦 + 5 − 2 = 𝑧 + 3 1 and 𝑥 + 1 − 3 = 𝑦 − 1 2 = 𝑧 + 3 2 .

Q10:

Find the vector form of the equation of the straight line passing through the point ( 2 , − 5 , − 5 ) and the centre of the sphere whose equation is 2 𝑥 + 2 𝑦 + 2 𝑧 + 1 2 𝑥 − 8 𝑦 + 8 𝑧 = 1 2 2 2 .

Q11:

Determine the vector form of the equation of the straight line passing through the point ( − 1 , − 5 , 4 ) and parallel to the vector ( − 3 , 5 , 1 ) .

Q12:

Determine, in vector form, the equation of the straight line that passes through the points ( − 5 , − 5 , 3 ) and ( − 3 , − 4 , 4 ) .

Q13:

Find the vector equation of the straight line that is parallel to the 𝑥 -axis and passing through the point ( − 5 , 2 ) .

Q14:

Consider the line through the point ( 0 , 4 ) and perpendicular to vector ⃑ 𝑟 = ( 0 , 4 ) . Which of the following is a vector equation of this line?

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