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In this lesson, we will learn how to determine the relationship between a straight line and a plane.

Q1:

Find the coordinates of the point of intersection of the straight line β π = ( 8 , 2 , β 5 ) + π‘ ( β 7 , β 9 , 1 3 ) with the plane ( 9 , 4 , β 5 ) β β π = β 5 9 .

Q2:

Find the coordinates of the point of intersection of the straight line β π = ( β 3 , β 4 , 7 ) + π‘ ( β 3 , 1 , β 9 ) with the plane ( β 3 , β 5 , 7 ) β β π = 1 9 .

Q3:

Find the coordinates of the point of intersection of the straight line β π = ( β 2 , β 9 , 6 ) + π‘ ( 8 , 5 , β 3 ) with the plane ( 9 , 4 , β 3 ) β β π = 2 9 .

Q4:

Find the coordinates of the point of intersection of the straight line β π = ( β 8 , 8 , 4 ) + π‘ ( 5 , β 3 , β 1 ) with the plane ( 8 , 7 , β 3 ) β β π = 2 4 .

Q5:

Straight line β ο© ο© ο© ο© β π΄ π΅ is parallel to plane π , and from a point π neither on the line nor in the plane are drawn rays ο« π π΄ , ο« π π΅ meeting π in π· and π» . If π π΄ π΄ π· = 2 9 : : , what is the ratio between π΄ π΅ and π· π» ?

Q6:

In the figure, π΄ π΅ lies in the plane π , and π΄ πΆ is perpendicular to π . Given that π΄ π΅ = 6 and π΄ πΆ = 8 , find the length of π΅ πΆ .

Q7:

π΄ π΅ πΆ is a triangle with π β π΅ = 6 0 β and π΅ πΆ = 2 3 . πΆ π· is drawn perpendicular to the plane of π΄ π΅ πΆ , and the perpendicular to π΄ π΅ from π· drawn to meet it at πΈ . If π· πΈ = 2 3 , determine the length of πΆ π· and the angle between π΅ π· and the plane of πΆ π· πΈ .

Q8:

Which of the following makes the straight line π₯ β π₯ π = π¦ β π¦ π = π§ β π§ π 1 1 1 lie on the plane π π₯ + π π¦ + π π§ + π = 0 ?

Q9:

Triangle is right angled at , and is orthogonal to the plane . A perpendicular is drawn from on . The area of is 1β134, , and . Let be the angle between and the plane . Find to the nearest thousandth.

Q10:

Find the point of intersection of the line π₯ β 6 4 = π¦ + 3 = π§ with the plane π₯ + 3 π¦ + 2 π§ β 6 = 0 .

Q11:

Find, to the nearest second, the measure of the smaller angle between the straight line π₯ β 7 7 = π¦ β 7 β 5 = π§ β 4 1 and the plane 6 π₯ β 8 π¦ β 5 π§ β 1 7 = 0 .

Q12:

The equation of a straight line is πΏ βΆ π₯ β 1 2 = π¦ + 9 β 7 = π§ + 5 β 5 and the equaton of a plane is π βΆ 8 π₯ β 2 8 π¦ β 2 0 π§ + 1 9 = 0 . Which of the following describes the relationship between πΏ and π ?

Q13:

The equation of a straight line is πΏ βΆ π₯ + 2 7 = π¦ β 7 7 = π§ + 5 8 and the equaton of a plane is π βΆ 7 π₯ + π¦ β 7 π§ β 2 8 = 0 . Which of the following describes the relationship between πΏ and π ?

Q14:

The equation of a straight line is πΏ βΆ π₯ β 1 9 = π¦ + 2 β 1 = π§ + 8 4 and the equaton of a plane is π βΆ β 5 π₯ β 9 π¦ + 9 π§ β 4 = 0 . Which of the following describes the relationship between πΏ and π ?

Q15:

The equation of a straight line is πΏ βΆ π₯ + 5 2 = π¦ β 3 3 = π§ β 9 2 and the equaton of a plane is π βΆ 6 π₯ + 9 π¦ + 6 π§ β 2 6 = 0 . Which of the following describes the relationship between πΏ and π ?

Q16:

The equation of a straight line is πΏ βΆ π₯ + 5 2 = π¦ β 3 5 = π§ + 6 9 and the equaton of a plane is π βΆ 2 π₯ + π¦ β π§ + 1 = 0 . Which of the following describes the relationship between πΏ and π ?

Q17:

What is π΄ πΆ β© π΄ β² πΆ β² ?

Q18:

In which of the following cases is the straight line β ο© ο© ο© ο© β π΄ π΅ parallel to the plane π ?

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