#### Chapters

Chapter 1.2: Matrics

Chapter 1.3: Trigonometric Functions

Chapter 1.4: Pair of Lines

Chapter 1.5: Vectors and Three Dimensional Geometry

Chapter 1.6: Line and Plane

Chapter 1.7: Linear Programming Problems

Chapter 2.1: Differentiation

Chapter 2.2: Applications of Derivatives

Chapter 2.3: Indefinite Integration

Chapter 2.4: Definite Integration

Chapter 2.5: Application of Definite Integration

Chapter 2.6: Differential Equations

Chapter 2.7: Probability Distributions

Chapter 2.8: Binomial Distribution

## 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 Multiple choice questions

#### 2 marks

The equation of X axis is ______

x = y = z

y = z

y = 0, z = 0

x = 0, y = 0

**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)`

**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

**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

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

−2

2

`(-1)/2`

`1/2`

**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)`

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

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

6

`6/sqrt(26)`

36

`1/sqrt(26)`

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 2021 Chapter 2 Line and Plane Very Short Answers

#### 1 mark

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

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

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

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")`

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

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"`

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 2021 Chapter 2 Line and Plane Short Answers I

#### 2 Marks

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)`

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

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

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

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

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

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 2021 Chapter 2 Line and Plane Short Answers II

#### 3 Marks

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"`

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

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

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

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

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

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

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`

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

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

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 2021 Chapter 2 Line and Plane Long Answers III

#### 4 Marks

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

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

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"`

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

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"`

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

## 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

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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.

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