NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 are part of NCERT Solutions for Class 12 Maths. Here we have given NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 12 |

Subject |
Maths |

Chapter |
Chapter 11 |

Chapter Name |
Three Dimensional Geometry |

Exercise |
Ex 11.2 |

Number of Questions Solved |
17 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2

**Question 1.**

Show that the three lines with direction cosines:

are mutually perpendicular.

**Solution:**

Let the lines be L1,L2 and L3.

∴ For lines L1 and L2

**Question 2.**

Show that the line through the points (1,-1,2) (3,4, -2) is perpendicular to the line through the points (0,3,2) and (3,5,6).

**Solution:**

Let A, B be the points (1, -1, 2), (3, 4, -2) respectively Direction ratios of AB are 2,5, -4

Let C, D be the points (0, 3, 2) and (3, 5, 6) respectively Direction ratios of CD are 3, 2,4 AB is Perpendicular to CD if

**Question 3.**

Show that the line through the points (4,7,8) (2,3,4) is parallel to the line through the points (-1,-2,1) and (1,2,5).

**Solution:**

Let the points be A(4,7,8), B (2,3,4), C (-1,-2,1) andD(1,2,5).

Now direction ratios of AB are

**Question 4.**

Find the equation of the line which passes through the point (1,2,3) and is parallel to the vector

**Solution:**

Equation of the line passing through the point

**Question 5.**

Find the equation of the line in vector and in cartesian form that passes through the point with position vector and is in the direction .

**Solution:**

The vector equation of a line passing through a point with position vector and parallel to the

**Question 6.**

Find the cartesian equation of the line which passes through the point (-2,4, -5) and parallel to the line is given by

**Solution:**

The cartesian equation of the line passing through the point (-2,4, -5) and parallel to the

**Question 7.**

The cartesian equation of a line is

write its vector form.

**Solution:**

The cartesian equation of the line is

Clearly (i) passes through the point (5, – 4, 6) and has 3,7,2 as its direction ratios.

=> Line (i) passes through the point A with

**Question 8.**

Find the vector and the cartesian equations of the lines that passes through the origin and (5,-2,3).

**Solution:**

The line passes through point

Direction ratios of the line passing through the

**Question 9.**

Find the vector and cartesian equations of the line that passes through the points (3, -2, -5), (3,-2,6).

**Solution:**

The PQ passes through the point P(3, -2, -5)

**Question 10.**

Find the angle between the following pair of lines

(i)

(ii)

**Solution:**

(i) Let θ be the angle between the given lines.

The given lines are parallel to the vectors

**Question 11.**

Find the angle between the following pair of lines

(i)

(ii)

**Solution:**

Given

(i)

(ii)

**Question 12.**

Find the values of p so that the lines

are at right angles

**Solution:**

The given equation are not in the standard form

The equation of given lines is

**Question 13.**

Show that the lines are perpendicular to each other

**Solution:**

Given lines

…(i)

…(ii)

**Question 14.**

Find the shortest distance between the lines

and

**Solution:**

The shortest distance between the lines

**Question 15.**

Find the shortest distance between the lines

**Solution:**

Shortest distance between the lines

**Question 16.**

Find the distance between die lines whose vector equations are:

and

**Solution:**

Comparing the given equations with

**Question 17.**

Find the shortest distance between the lines whose vector equations are

and

**Solution:**

Comparing these equation with

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