What is the relation between the plane ax + by + cz + d = 0 and a1, b1, c1 the direction ratios of a line, if the plane and line are perpendicular to each other?

( frac {c1}{a2} = frac{b1}{b2} = frac{a1}{c2} )

( frac {a1}{b1} = frac{a2}{c1} = frac{c2}{b2} )

( frac {a1}{a2} = frac{b1}{c2} = frac{c1}{b2} )

( frac {a}{a1} = frac{b}{b1} = frac{c}{c1} )

( frac {c1}{a2} = frac{b1}{b2} = frac{a1}{c2} )

What is the plane equation involved in the formula sin = ( frac {a1a+b1b+c1c}{ sqrt {a^2+b^2+c^2} sqrt{a1^2+b1^2+c1^2 }} )?

a1x + b1y + c1z + d1 = 0 and ax + by + cz + d = 0

_____ is the complement of the angle between the line L and a normal line to the plane .

Tangent between a plane and a line

Normal between a plane and a line

The angle between a line and a plane

Tangent between a plane and a line

Distance between a plane and a line

15 + Mcqs in Three Dimensional Geometry Angle between a Line and a Plane in Mathematics Page 1 McqOptions

1.	Find k for the given plane x + 2y + kz + 2 = 0 and directional ratios of a line (8, 3, 2), if they are parallel to each other.
A.	21
B.	-17
C.	12
D.	-7
Answer» E.

Discussion

2.	Find the angle between the planes 5x + 2y + 3z + 1 = 0 and (1, 1, -2).
A.	30.82
B.	3.43
C.	11.23
D.	7.54
Answer» C. 11.23

Discussion

3.	The plane 5x + y + kz + 1 = 0 and directional ratios of a line (3, -1, 1) are parallel, find k.
A.	4
B.	-14
C.	6
D.	-8
Answer» C. 6

Discussion

4.	Find the angle between x + 2y + 7z + 2 = 0 and (2, 4, 6).
A.	69.69
B.	84.32
C.	66.92
D.	83.25
Answer» D. 83.25

Discussion

5.	Find the angle between 2x + 3y 2z + 4 = 0 and (2, 1, 1).
A.	38.2
B.	19.64
C.	89.21
D.	29.34
Answer» E.

Discussion

6.	The condition ( frac {a}{a1} = frac{b}{b1} = frac{c}{c1} ) is for a plane and a line are _____ to each other.
A.	perpendicular
B.	parallel
C.	differential
D.	tangential
Answer» B. parallel

Discussion

7.	The condition a₁a + b₁b + c₁c = 0 is for a plane and a line are _____ to each other.
A.	integral
B.	parallel
C.	perpendicular
D.	concentric
Answer» C. perpendicular

Discussion

8.	A plane and a line having an angle of 90 degrees between them are called _____
A.	Orthogonal
B.	Tangential
C.	Normal
D.	Parallel
Answer» B. Tangential

Discussion

9.	What is the relation between the plane ax + by + cz + d = 0 and a₁, b₁, c₁ the direction ratios of a line, if the plane and line are parallel to each other?
A.	a<sub>1</sub>a<sub>2</sub> . b<sub>1</sub>b<sub>2</sub> . c<sub>1</sub>c<sub>2</sub> = 0
B.	a<sub>1</sub>a + b<sub>1</sub>b + c<sub>1</sub>c = 0
C.	a<sub>1</sub>a<sub>2</sub> + b<sub>1</sub>b<sub>2</sub> c<sub>1</sub>c<sub>2</sub> = 0
D.	a<sub>1</sub>a<sub>2</sub> + b<sub>1</sub>b<sub>2</sub> c<sub>1</sub>c<sub>2</sub> = 0
Answer» C. a<sub>1</sub>a<sub>2</sub> + b<sub>1</sub>b<sub>2</sub> c<sub>1</sub>c<sub>2</sub> = 0

Discussion

10.	What is the relation between the plane ax + by + cz + d = 0 and a₁, b₁, c₁ the direction ratios of a line, if the plane and line are perpendicular to each other?
A.	( frac {a1}{b1} = frac{a2}{c1} = frac{c2}{b2} )
B.	( frac {a1}{a2} = frac{b1}{c2} = frac{c1}{b2} )
C.	( frac {a}{a1} = frac{b}{b1} = frac{c}{c1} )
D.	( frac {c1}{a2} = frac{b1}{b2} = frac{a1}{c2} )
Answer» D. ( frac {c1}{a2} = frac{b1}{b2} = frac{a1}{c2} )

Discussion

11.	What is the plane equation involved in the formula sin = ( frac {a1a+b1b+c1c}{ sqrt {a^2+b^2+c^2} sqrt{a1^2+b1^2+c1^2 }} )?
A.	a<sub>1</sub>x b<sub>1</sub>y + c<sub>1</sub>z + d<sub>1</sub> = 0
B.	a<sub>1</sub>x<sup>2</sup> + b<sub>1</sub>y<sup>2</sup> + c<sub>1</sub>z<sup>2</sup> + d<sub>1</sub> = 0
C.	ax + by + cz+ d = 0
D.	a<sub>1</sub>x + b<sub>1</sub>y + c<sub>1</sub>z + d<sub>1</sub> = 0 and ax + by + cz + d = 0
Answer» D. a<sub>1</sub>x + b<sub>1</sub>y + c<sub>1</sub>z + d<sub>1</sub> = 0 and ax + by + cz + d = 0

Discussion

12.	Which trigonometric function is used to find the angle between a line and a plane?
A.	Tangent
B.	Cosecant
C.	Secant
D.	Sine
Answer» E.

Discussion

13.	Find the angle between the planes x + 2y + 3z + 1 = 0 and (4, 1, -7).
A.	29.34
B.	3.43
C.	11.23
D.	17.54
Answer» B. 3.43

Discussion

14.	If is the angle between line whose ratios are a₁, b₁, c₁ and the plane ax + by + cz + d = 0 then cos = ( frac {a1a2.b1b2.c1c2}{ sqrt {a1^2+b1^2+c1^2} sqrt {a2^2+b2^2+c2^2 }} ).
A.	True
B.	False
Answer» C.

Discussion

15.	_____ is the complement of the angle between the line L and a normal line to the plane .
A.	Normal between a plane and a line
B.	The angle between a line and a plane
C.	Tangent between a plane and a line
D.	Distance between a plane and a line
Answer» C. Tangent between a plane and a line

Discussion

Explore topic-wise MCQs in Mathematics.

Find k for the given plane x + 2y + kz + 2 = 0 and directional ratios of a line (8, 3, 2), if they are parallel to each other.

Find the angle between the planes 5x + 2y + 3z + 1 = 0 and (1, 1, -2).

The plane 5x + y + kz + 1 = 0 and directional ratios of a line (3, -1, 1) are parallel, find k.

Find the angle between x + 2y + 7z + 2 = 0 and (2, 4, 6).

Find the angle between 2x + 3y 2z + 4 = 0 and (2, 1, 1).

The condition ( frac {a}{a1} = frac{b}{b1} = frac{c}{c1} ) is for a plane and a line are _____ to each other.

The condition a1a + b1b + c1c = 0 is for a plane and a line are _____ to each other.

A plane and a line having an angle of 90 degrees between them are called _____

What is the relation between the plane ax + by + cz + d = 0 and a1, b1, c1 the direction ratios of a line, if the plane and line are parallel to each other?

What is the relation between the plane ax + by + cz + d = 0 and a1, b1, c1 the direction ratios of a line, if the plane and line are perpendicular to each other?

What is the plane equation involved in the formula sin = ( frac {a1a+b1b+c1c}{ sqrt {a^2+b^2+c^2} sqrt{a1^2+b1^2+c1^2 }} )?

Which trigonometric function is used to find the angle between a line and a plane?

Find the angle between the planes x + 2y + 3z + 1 = 0 and (4, 1, -7).

If is the angle between line whose ratios are a1, b1, c1 and the plane ax + by + cz + d = 0 then cos = ( frac {a1a2.b1b2.c1c2}{ sqrt {a1^2+b1^2+c1^2} sqrt {a2^2+b2^2+c2^2 }} ).

_____ is the complement of the angle between the line L and a normal line to the plane .

The condition a₁a + b₁b + c₁c = 0 is for a plane and a line are _____ to each other.

What is the relation between the plane ax + by + cz + d = 0 and a₁, b₁, c₁ the direction ratios of a line, if the plane and line are parallel to each other?

What is the relation between the plane ax + by + cz + d = 0 and a₁, b₁, c₁ the direction ratios of a line, if the plane and line are perpendicular to each other?

If is the angle between line whose ratios are a₁, b₁, c₁ and the plane ax + by + cz + d = 0 then
cos = ( frac {a1a2.b1b2.c1c2}{ sqrt {a1^2+b1^2+c1^2} sqrt {a2^2+b2^2+c2^2 }} ).