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CBSE Class 12 Math 2019 All India Set 1 Solved Paper

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Question : 4 of 29
Marks: +1, -0
If a line has the direction ratios −18,12,−4-18,12,-4, then what are its direction cosines?
OR
Find the cartesian equation of the line which passes through the point (−2,4,−5)(-2,4,-5) and is parallel to the line   x+33=  4−y5=  z+86\;\frac{x+3}{3} = \;\frac{4-y}{5} = \;\frac{z+8}{6}.
Solution:  
Direction ratios of a line are −18,12,−4-18,12,-4
Direction cosines of line are −  18182+122+42,  12182+122+42,−  4182+122+42-\;\frac{18}{\sqrt{18^2+12^2+4^2}}, \;\frac{12}{\sqrt{18^2+12^2+4^2}},-\;\frac{4}{\sqrt{18^2+12^2+4^2}}
Hence, direction cosines of line are −  911,  611,−  211-\;\frac{9}{11}, \;\frac{6}{11},-\;\frac{2}{11}.
OR
The cartesian equation of the line which passes through the point (−2,4,−5)(-2,4,-5) and is parallel to the line   x+33=  y−4−5=  z+86\;\frac{x+3}{3} = \;\frac{y-4}{-5} = \;\frac{z+8}{6} is   x+23=  y−4−5=  z+56\;\frac{x+2}{3} = \;\frac{y-4}{-5} = \;\frac{z+5}{6}.
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