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NCERT Solutions for Class 12 Help.html Mathematics Part Ii Chapter 11 Three Dimensional Geometry

Three Dimensional Geometry Here is the CBSE Help.html Chapter 11 for Class 12 students. Summary and detailed explanation of the lesson, including the definitions of difficult words. All of the exercises and questions and answers from the lesson's back end have been completed. NCERT Solutions for Class 12 Help.html Three Dimensional Geometry Chapter 11 NCERT Solutions for Class 12 Help.html Three Dimensional Geometry Chapter 11 The following is a summary in Hindi and English for the academic year 2025-26. You can save these solutions to your computer or use the Class 12 Help.html.

Question 1
CBSEENMA12033219
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If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines.

Solution
Let l, m, n be the direction cosines of the line with direction angles 90°, 135°, 45°.
therefore space space straight l space equals space cos space 90 degree space equals space 0 comma space space space straight m space equals space cos space 135 degree space equals space cos space left parenthesis 180 degree minus 45 degree right parenthesis space equals space minus cos space 45 degree space equals space minus fraction numerator 1 over denominator square root of 2 end fraction comma
           straight n space equals space cos space 45 degree space equals space fraction numerator 1 over denominator square root of 2 end fraction
therefore space space   direction cosines are 0,  negative fraction numerator 1 over denominator square root of 2 end fraction comma space fraction numerator 1 over denominator square root of 2 end fraction.

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