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D Divya Prakash Singh
Given vertices of the triangle   (3, 5, – 4), (– 1, 1, 2) and (– 5, – 5, – 2). Finding each side direction ratios; Direction ratios of side AB are  i.e., Therefore its direction cosines values are;   SImilarly for side BC;     Direction ratios of side BC are  i.e., Therefore its direction cosines values are;     Direction ratios of side CA are  i.e., Therefore its direction cosines values are;  

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D Divya Prakash Singh
We have the points,  A (2, 3, 4),B (– 1, – 2, 1),C (5, 8, 7); And as we can find the direction ratios of the line joining the points  is given by   The direction ratios of AB are  i.e.,  The direction ratios of BC are  i.e., . We can see that the direction ratios of AB and BC are proportional to each other and is -2 times.  AB is parallel to BC. and as point B is common to both AB and BC, Hence...

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D Divya Prakash Singh
GIven a line has direction ratios of -18, 12, – 4 then its direction cosines are; Line having direction ratio -18 has direction cosine:  Line having direction ratio 12 has direction cosine: Line having direction ratio -4 has direction cosine: Thus, the direction cosines are .  

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D Divya Prakash Singh
If the line is making equal angle with the coordinate axes. Then, Let the common angle made is  with each coordinate axes. Therefore, we can write; And as we know the relation;  or  Thus the direction cosines of the line are   .  

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D Divya Prakash Singh
Let the direction cosines of the line be l,m, and n. So, we have         Therefore the direction cosines of the lines are .
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