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In this lesson, we will learn how to calculate the distance between a point and a straight line or between a point and a plane using a formula for each distance.

Q1:

Find, to one decimal place, the perpendicular distance from point ( β 3 , β 4 , 0 ) to the line on points ( 1 , 3 , 1 ) and ( 4 , 3 , 2 ) .

Q2:

Find the distance from the point π = ( 0 , 2 , 0 ) to the plane π βΆ β 5 π₯ + 2 π¦ β 7 π§ + 1 = 0 . Give the result correct to three decimal places.

Q3:

Determine the length of the perpendicular from a point π΄ ( 0 , 0 ) to the line π π₯ + π π¦ + π = 0 .

Q4:

Find the distance between the point ( 2 , β 1 , 3 ) and the plane β π β ( β 2 , 2 , 1 ) = 3 .

Q5:

Find the distance between the two planes β π₯ β 2 π¦ β 2 π§ = β 2 and β 2 π₯ β 4 π¦ β 4 π§ = 3 .

Q6:

Find the distance from the point π = ( 4 , 1 , 2 ) to the plane π : 3 π₯ β π¦ β 5 π§ + 8 = 0 , giving your answer to two decimal places.

Q7:

Find, correct to two decimal places, the distance π from the point π = ( 1 , β 1 , β 1 ) to the line πΏ π₯ = β 2 β 2 π‘ , π¦ = 4 π‘ , π§ = 7 + π‘ : .

Q8:

Find, correct to two decimal places, the distance from the point π = ( 0 , 0 , 0 ) to the line πΏ βΆ π₯ = 3 + 2 π‘ , π¦ = 4 + 3 π‘ , π§ = 5 + 4 π‘ .

Q9:

Find the length of the perpendicular from the point ( 5 , 7 ) to the straight line β π = ( β 7 , 6 ) + π ( β 5 , 7 ) .

Q10:

Find the length of the perpendicular from the origin to the straight line β π = ( β 7 , β 9 ) + π ( 5 , β 5 ) .

Q11:

How far from the π¦ π§ -plane is the point ( β 1 6 , β 1 3 , 2 0 ) ?

Q12:

Find the distance between the point ( β 5 , β 8 , β 6 ) and the plane β 2 π₯ + π¦ + 2 π§ = 7 .

Q13:

Find, to one decimal place, the perpendicular distance from point ( β 3 , β 3 , 2 ) to the line on points ( β 2 , 0 , 4 ) and ( 0 , β 5 , 2 ) .

Q14:

Find, to one decimal place, the perpendicular distance from point ( 4 , β 1 , 3 ) to the line on points ( 0 , β 4 , β 4 ) and ( β 5 , 4 , β 3 ) .

Q15:

Find the distance between the point ( 4 , β 2 , 2 ) and the plane β π β ( β 2 , 2 , 1 ) = β 4 .

Q16:

Find the distance between the point ( β 3 , β 4 , 2 ) and the plane β π β ( β 4 , 4 , β 2 ) = β 2 .

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