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SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 2 - Line and Plane [Latest edition]

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Chapters

12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 - Shaalaa.com

Chapter 2: Line and Plane

Multiple choice questionsVery Short AnswersShort Answers IShort Answers IILong Answers III
Multiple choice questions

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 2 Line and Plane Multiple choice questions

2 marks

Multiple choice questions | Q 1

The equation of X axis is ______ 

  • x = y = z

  • y = z

  • y = 0, z = 0

  • x = 0, y = 0

Multiple choice questions | Q 2

Choose correct alternatives :

The perpendicular distance of the plane 2x + 3y – z = k from the origin is `sqrt(14)` units, the value of k is ______ 

  • 14

  • 196

  • `2sqrt(14)`

  • `sqrt(14)/(2)`

Multiple choice questions | Q 3

Choose correct alternatives :

The equation of the plane passing through the points (1, −1, 1), (3, 2, 4) and parallel to the Y-axis is ______  

  • 3x + 2z – 1 = 0

  • 3x – 2z = 1

  • 3x + 2z + 1 = 0

  • 3x + 2z = 2

Multiple choice questions | Q 4

Choose correct alternatives :

The direction ratios of the line 3x + 1 = 6y – 2 = 1 – z are ______ 

  • 2, 1, 6

  • 2, 1, – 6

  • 2, – 1, 6

  • – 2, 1, 6

Multiple choice questions | Q 5

If the planes 2x – my + z = 3 and 4x – y + 2z = 5 are parallel then m = ______ 

  • −2

  • 2

  • `(-1)/2`

  • `1/2`

Multiple choice questions | Q 6

Choose correct alternatives :

The direction cosines of the normal to the plane 2x – y + 2z = 3 are ______ 

  • `(2)/(3),(-1)/(3),(2)/(3)`

  • `(-2)/(3),(1)/(3),(-2)/(3)`

  • `(2)/(3),(1)/(3),(2)/(3)`

  • `(2)/(3),(-1)/(3),(-2)/(3)`

Multiple choice questions | Q 7

If the foot of the perpendicular drawn from the origin to the plane is (4, −2, 5), then the equation of the plane is ______ 

  • 4x + y + 5z = 14

  • 4x − 2y − 5z = 45

  • x − 2y − 5z =10

  • 4x + y + 6z = 11

Multiple choice questions | Q 8

The perpendicular distance of the origin from the plane x − 3y + 4z = 6 is ______ 

  • 6

  • `6/sqrt(26)`

  • 36

  • `1/sqrt(26)`

Multiple choice questions | Q 9

The coordinates of the foot of perpendicular drawn from the origin to the plane 2x + y − 2z = 18 are ______ 

  • (4, 2, 4)

  • (−4, 2, 4)

  • (−4, −2, 4)

  • (4, 2, −4)

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Very Short Answers

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 2 Line and Plane Very Short Answers

1 mark

Very Short Answers | Q 1

Find the Cartesian equation of a plane passing through A(1, 2, 3) and direction ratios of it’s normal are 3, 2, 5

Very Short Answers | Q 2

Find the direction ratios of the normal to the plane 2x + 3y + z = 7

Very Short Answers | Q 3

Find the vector equation of the line `x/1 = (y - 1)/2 = (z - 2)/3`

Very Short Answers | Q 4

Verify if the point having position vector `4hat"i" - 11hat"j" + 2hat"k"` lies on the line `bar"r" = (6hat"i" - 4hat"j" + 5hat"k") + mu (2hat"i" + 7hat"j" + 3hat"k")`

Very Short Answers | Q 5

Find the Cartesian equation of the line passing through  A(1, 2, 3) and having direction ratios 2, 3, 7

Very Short Answers | Q 6

Find the vector equation of the line passing through the point having position vector `4hat"i" - hat"j" + 2hat"k"` and parallel to the vector `-2hat"i" - hat"j" + hat"k"`

Very Short Answers | Q 7

Find the Cartesian equation of the plane passing through the points (3, 2, 1) and (1, 3, 1)

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Short Answers I

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 2 Line and Plane Short Answers I

2 Marks

Short Answers I | Q 1

Find the direction ratios of the line perpendicular to the lines

`(x - 7)/2 = (y + 7)/(-3) = (z - 6)/1` and `(x + 5)/1 = (y + 3)/2 = (z - 6)/(-2)`

Short Answers I | Q 2

Find direction cosines of the normal to the plane `bar"r"*(3hat"i" + 4hat"k")` = 5

Short Answers I | Q 3

If the normal to the plane has direction ratios 2, −1, 2 and it’s perpendicular distance from origin is 6, find its equation

Short Answers I | Q 4

Reduce the equation `bar"r"*(3hat"i" + 4hat"j" + 12hat"k")` = 8 to normal form

Short Answers I | Q 5

Find the Cartesian equation of the line passing through A(1, 2, 3) and B(2, 3, 4)

Short Answers I | Q 6

Find the perpendicular distance of origin from the plane 6x − 2y + 3z - 7 = 0

Short Answers I | Q 7

Find the acute angle between the lines x = y, z = 0 and x = 0, z = 0

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Short Answers II

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 2 Line and Plane Short Answers II

3 Marks

Short Answers II | Q 1

Find Cartesian equation of the line passing through the point A(2, 1, −3) and perpendicular to vectors `hat"i" + hat"j" + hat"k"` and `hat"i" + 2hat"j" - hat"k"`

Short Answers II | Q 2

Find the vector equation of the line passing through the point having position vector `-hat"i"- hat"j" + 2hat"k"` and parallel to the line `bar"r" = (hat"i" + 2hat"j" + 3hat"k") + mu(3hat"i" + 2hat"j" + hat"k")`, µ is a parameter

Short Answers II | Q 3

Find the Cartesian equation of the line passing through (−1, −1, 2) and parallel to the line 2x − 2 = 3y + 1 = 6z – 2

Short Answers II | Q 4

Find the Cartesian equation of the plane passing through A(7, 8, 6)and parallel to XY plane

Short Answers II | Q 5

Find the coordinates of the foot of perpendicular from the origin to the plane 2x + 6y − 3z = 63

Short Answers II | Q 6

Find the vector equation of a plane at a distance 6 units from the origin and to which vector `2hat"i" - hat"j" + 2hat"k"` is normal

Short Answers II | Q 7

Find the Cartesian equation of the plane passing through the points A(1, 1, 2), B(0, 2, 3) C(4, 5, 6)

Short Answers II | Q 8

Find acute angle between the lines `(x - 1)/1 = (y - 2)/(-1) = (z - 3)/2` and `(x - 1)/2 = (y - 1)/1 = (z - 3)/1`

Short Answers II | Q 9

Find the distance between the parallel lines `x/2 = y/(-1) = z/2` and `(x - 1)/2 = (y - 1)/(-1) = (z - 3)/2`

Short Answers II | Q 10

Find the equation of the plane passing through the point (7, 8, 6) and parallel to the plane `bar"r"*(6hat"i" + 8hat"j" + 7hat"k")` = 0

Short Answers II | Q 11

Find m, if the lines `(1 - x)/3 =(7y - 14)/(2"m") = (z - 3)/2` and `(7 - 7x)/(3"m") = (y - 5)/1 = (6 - z)/5` are at right angles

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Long Answers III

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 2 Line and Plane Long Answers III

4 Marks

Long Answers III | Q 1

Show that the lines `(x + 1)/(-10) = (y + 3)/(-1) = (z - 4)/(1)` and `(x + 10)/(-1) = (y + 1)/(-3) = (z - 1)/4` intersect each other.also find the coordinates of the point of intersection

Long Answers III | Q 2

A(– 2, 3, 4), B(1, 1, 2) and C(4, –1, 0) are three points. Find the Cartesian equations of the line AB and show that points A, B, C are collinear

Long Answers III | Q 3

Find the Cartesian and vector equation of the line passing through the point having position vector `hat"i" + 2hat"j" + 3hat"k"` and perpendicular to vectors `hat"i" + hat"j" + hat"k"` and `2hat"i" - hat"j" + hat"k"`

Long Answers III | Q 4

Find the vector equation of the plane which bisects the segment joining A(2, 3, 6) and B(4, 3, −2) at right angles

Long Answers III | Q 5

Find vector equation of the plane passing through A(−2 ,7 ,5) and parallel to vectors `4hat"i"  - hat"j" + 3hat"k"` and `hat"i" + hat"j" + hat"k"`

Long Answers III | Q 6

Find the Cartesian and vector equation of the plane which makes intercepts 1, 1, 1 on the coordinate axes

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Chapter 2: Line and Plane

Multiple choice questionsVery Short AnswersShort Answers IShort Answers IILong Answers III
12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 - Shaalaa.com

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 2 - Line and Plane

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 2 (Line and Plane) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 2 Line and Plane are Vector and Cartesian Equations of a Line, Distance of a Point from a Line, Skew Lines, Equations of Plane, Angle Between Planes, Coplanarity of Two Lines, Distance of a Point from a Plane.

Using SCERT Maharashtra Question Bank 12th Board Exam solutions Line and Plane exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in SCERT Maharashtra Question Bank Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board 12th Board Exam prefer SCERT Maharashtra Question Bank Textbook Solutions to score more in exam.

Get the free view of chapter 2 Line and Plane 12th Board Exam extra questions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 and can use Shaalaa.com to keep it handy for your exam preparation

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