# SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 2 - Line and Plane [Latest edition]

## Chapter 2: Line and Plane

Multiple choice questions

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 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)

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 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)

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 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

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 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

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 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

## SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 2 - Line and Plane

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 2 Line and Plane are Vector and Cartesian Equations of a Line, Angle Between Planes, Coplanarity of Two Lines, Distance of a Point from a Plane, Distance Between Skew Lines and Parallel Lines, Distance of a Point from a Line, Equation of a Plane.

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