NCERT Solutions class 12 Maths Exercise 11.1

NCERT Solutions class 12 Maths Exercise 11.1 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

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NCERT Solutions class 12 Maths Three Dimensional Geometry 

1.If a line makes angles  with the  and axes respectively, find its direction cosines.

Ans. Here and

Since direction cosines of a line making angles  with the  and axes respectively are

Therefore, direction cosines of the required line are  and  = 0,  and  

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NCERT Solutions class 12 Maths Exercise 11.1

2.Find the direction cosines of a line which makes equal angles with the co-ordinate axes.

Ans. Let a line make equal angles  with the co-ordinate axes.

Direction cosines of the line are ……….(i)

Putting  in eq. (i), direction cosines of the required line making equal angles with the co-ordinate axes are

Direction cosines of a line making equal angles with the co-ordinate axes in the positive i.e., first octant are

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NCERT Solutions class 12 Maths Exercise 11.1

3.If a line has direction ratios , then what are its direction cosines?

Ans. We know that if  are direction ratios of a line, then direction cosines of the line are:

……….(i)

Here direction ratios of the line are

Putting the values in eq. (i),

Hence, direction cosines of required line are .

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NCERT Solutions class 12 Maths Exercise 11.1

4.Show that the points (2, 3, 4),  (5, 8, 7) are collinear.

Ans. The given points are A (2, 3, 4), B and C (5, 8, 7)

Direction ratios of the line joining A and B are

 …….(i)

  =  (say)

Again Direction ratios of the line joining B and C are

 =  (say)……….(ii)

From eq. (i) and (ii),

Therefore, AB is parallel to BC. But point B is common to both AB and BC. Hence points A, B, C are collinear.

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NCERT Solutions class 12 Maths Exercise 11.1

5.Find the direction cosines of the sides of the triangle whose vertices are  and  

Ans. Direction ratios of the line joining A and B are

Direction cosines of line AB are

Now Direction ratios of the line joining B and C are

Direction cosines of line BC are

Direction ratios of the line joining C and A are

Direction cosines of line CA are

NCERT Solutions class 12 Maths Exercise 11.1

NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 13 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide

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