In this chapter, we provide NCERT Solutions for Class 12 Maths for English medium students, Which will very helpful for every student in their exams. Students can download the latest NCERT Solutions for Class 12 Maths pdf, free NCERT solutions for Class 12 Maths book pdf download.

Board | CBSE |

Textbook | NCERT |

Class | Class 12 |

Subject | Maths |

Chapter | Chapter 11 |

Chapter Name | Three Dimensional Geometry |

Exercise | Ex 11.1 |

Number of Questions Solved | 5 |

Category | NCERT Solutions |

## NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1

**Ex 11.1 Class 12 Maths Question 1.**

If a line makes angles 90°, 135°, 45° with the and z axes respectively, find its direction cosines.**Solution:**

Direction angles are 90°, 135°, 45°

Direction cosines are

**Ex 11.1 Class 12 Maths Question 2.**

Find the direction cosines of a line which makes equal angles with coordinate axes.**Solution:**

Let direction angle be α each

∴ Direction cosines are cos α, cos α, cos α

But l² + m² + n² = 1

∴cos² a + cos² a + cos² a = 1

**Ex 11.1 Class 12 Maths Question 3.**

If a line has the direction ratios – 18,12, -4 then what are its direction cosines?**Solution:**

Now given direction ratios of a line are -8,12,-4

∴ a = -18,b = 12,c = -4

Direction cosines are

**Ex 11.1 Class 12 Maths Question 4.**

Show that the points (2,3,4) (-1,-2,1), (5,8,7) are collinear.**Solution:**

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

Let direction ratios of AB be

**Ex 11.1 Class 12 Maths Question 5.**

Find the direction cosines of the sides of the triangle whose vertices are (3,5, -4), (-1,1,2) and (-5,-5,-2).**Solution:**

The vertices of triangle ABC are A (3, 5, -4), B (-1,1,2), C (-5, -5, -2)

(i) Direction ratios of AB are (-4,-4,6)

Direction cosines are

**All Chapter NCERT Solutions For Class12 Maths**

—————————————————————————–**All Subject NCERT Solutions For Class12**

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