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Worksheet: Relationship between a Straight Line and a Plane

Q1:

Find the coordinates of the point of intersection of the straight line with the plane .

  • A
  • B
  • C
  • D
  • E

Q2:

Find the coordinates of the point of intersection of the straight line with the plane .

  • A
  • B
  • C
  • D
  • E

Q3:

Find the coordinates of the point of intersection of the straight line with the plane .

  • A
  • B
  • C
  • D
  • E

Q4:

Find the coordinates of the point of intersection of the straight line with the plane .

  • A
  • B
  • C
  • D
  • E

Q5:

Straight line 𝐴 𝐵 is parallel to plane 𝑋 , and from a point 𝑀 neither on the line nor in the plane are drawn rays 𝑀 𝐴 , 𝑀 𝐵 meeting 𝑋 in 𝐷 and 𝐻 . If 𝑀 𝐴 𝐴 𝐷 = 2 9 : : , what is the ratio between 𝐴 𝐵 and 𝐷 𝐻 ?

  • A 9 2
  • B 2 9
  • C 1 1 2
  • D 2 1 1

Q6:

In the figure, 𝐴 𝐵 lies in the plane 𝑋 , and 𝐴 𝐶 is perpendicular to 𝑋 . Given that 𝐴 𝐵 = 6 and 𝐴 𝐶 = 8 , find the length of 𝐵 𝐶 .

Q7:

𝐴 𝐵 𝐶 is a triangle with 𝑚 𝐵 = 6 0 and 𝐵 𝐶 = 2 3 . 𝐶 𝐷 is drawn perpendicular to the plane of 𝐴 𝐵 𝐶 , and the perpendicular to 𝐴 𝐵 from 𝐷 drawn to meet it at 𝐸 . If 𝐷 𝐸 = 2 3 , determine the length of 𝐶 𝐷 and the angle between 𝐵 𝐷 and the plane of 𝐶 𝐷 𝐸 .

  • A19.92, 4 0 5 3 3 6 . 2 2
  • B30.43, 3 0
  • C19.92, 6 3 2 6 5 . 8 2
  • D11.5, 2 6 3 3 5 4 . 1 8
  • E11.5, 6 3 2 6 5 . 8 2

Q8:

Which of the following makes the straight line 𝑥 𝑥 𝑙 = 𝑦 𝑦 𝑚 = 𝑧 𝑧 𝑛 1 1 1 lie on the plane 𝑎 𝑥 + 𝑏 𝑦 + 𝑐 𝑧 + 𝑑 = 0 ?

  • A 𝑎 𝑙 + 𝑏 𝑚 + 𝑐 𝑛 = 0
  • B 𝑎 𝑥 + 𝑏 𝑦 + 𝑐 𝑧 = 0 1 1 1
  • C ( 𝑙 , 𝑚 , 𝑛 ) × ( 𝑎 , 𝑏 , 𝑐 ) = 0
  • D 𝑎 𝑙 + 𝑏 𝑚 + 𝑐 𝑛 = 0 and 𝑎 𝑥 + 𝑏 𝑦 + 𝑐 𝑧 = 0 1 1 1
  • E ( 𝑙 , 𝑚 , 𝑛 ) ( 𝑎 , 𝑏 , 𝑐 ) 0

Q9:

Triangle is right at , and is orthogonal to the plane . A perpendicular is drawn from on . The area of is 1 134, , and . Let be the angle between and the plane . Find to the nearest thousandth.

  • A3.429
  • B0.247
  • C0.971
  • D4.045

Q10:

Find the point of intersection of the line 𝑥 6 4 = 𝑦 + 3 = 𝑧 with the plane 𝑥 + 3 𝑦 + 2 𝑧 6 = 0 .

  • A ( 2 , 4 , 1 )
  • B ( 2 , 4 , 1 )
  • C ( 2 4 , 3 , 0 )
  • D ( 1 0 , 2 , 1 )
  • E ( 1 8 , 0 , 3 )

Q11:

Find, to the nearest second, the size of the smaller angle between the straight line and the plane .

  • A
  • B
  • C
  • D

Q12:

The equation of a straight line is 𝐿 𝑥 1 2 = 𝑦 + 9 7 = 𝑧 + 5 5 and the equaton of a plane is 𝑃 8 𝑥 2 8 𝑦 2 0 𝑧 + 1 9 = 0 . Which of the following describes the relationship between 𝐿 and 𝑃 ?

  • A 𝐿 𝑃
  • B 𝐿 𝑃
  • CThey meet at a point but are not perpendicular.
  • D 𝐿 𝑃 and they do not intersect.

Q13:

The equation of a straight line is 𝐿 𝑥 + 2 7 = 𝑦 7 7 = 𝑧 + 5 8 and the equaton of a plane is 𝑃 7 𝑥 + 𝑦 7 𝑧 2 8 = 0 . Which of the following describes the relationship between 𝐿 and 𝑃 ?

  • A 𝐿 𝑃
  • B 𝐿 𝑃
  • CThey meet at a point but are not perpendicular.
  • D 𝐿 𝑃 and they do not intersect.

Q14:

The equation of a straight line is 𝐿 𝑥 1 9 = 𝑦 + 2 1 = 𝑧 + 8 4 and the equaton of a plane is 𝑃 5 𝑥 9 𝑦 + 9 𝑧 4 = 0 . Which of the following describes the relationship between 𝐿 and 𝑃 ?

  • A 𝐿 𝑃
  • B 𝐿 𝑃
  • CThey meet at a point but are not perpendicular.
  • D 𝐿 𝑃 and they do not intersect.

Q15:

The equation of a straight line is 𝐿 𝑥 + 5 2 = 𝑦 3 3 = 𝑧 9 2 and the equaton of a plane is 𝑃 6 𝑥 + 9 𝑦 + 6 𝑧 2 6 = 0 . Which of the following describes the relationship between 𝐿 and 𝑃 ?

  • A 𝐿 𝑃
  • B 𝐿 𝑃
  • CThey meet at a point but are not perpendicular.
  • D 𝐿 𝑃 and they do not intersect.

Q16:

The equation of a straight line is 𝐿 𝑥 + 5 2 = 𝑦 3 5 = 𝑧 + 6 9 and the equaton of a plane is 𝑃 2 𝑥 + 𝑦 𝑧 + 1 = 0 . Which of the following describes the relationship between 𝐿 and 𝑃 ?

  • A 𝐿 𝑃
  • B 𝐿 𝑃
  • CThey meet at a point but are not perpendicular.
  • D 𝐿 𝑃 and they do not intersect.

Q17:

What is 𝐴 𝐶 𝐴 𝐶 ?

  • A 𝐴 𝐴
  • B 𝐶 𝐶
  • C 𝐴 𝐶
  • D

Q18:

In which of the following cases is the straight line 𝐴 𝐵 parallel to the plane 𝑋 ?

  • A 𝐴 𝐵 𝑋 = 𝐴 𝐵
  • B 𝐴 𝐵 𝑋 = { 𝐵 }
  • C 𝐴 𝐵 𝑋 = { 𝐴 }
  • D 𝐴 𝐵 𝑋 =
  • E 𝐴 𝐵 𝑋