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Find the cartesian equation of the line which passes through the point `(2,4,5)`and parallel to the line given by `(x+3)/3=(y-4)/5=(z+8)/6`.

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To find the Cartesian equation of the line that passes through the point \( (2, 4, 5) \) and is parallel to the line given by the equation \[ \frac{x + 3}{3} = \frac{y - 4}{5} = \frac{z + 8}{6}, \] we can follow these steps: ...
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NCERT-THREE DIMENSIONAL GEOMETRY-EXERCISE 11.2
  1. Show that the three lines with direction cosines (12)/(13),(-3)/(13),...

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  2. Show that the line through the points (4, 7, 8), (2, 3, 4)is parallel...

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  3. Show that the line through the points (1, 1, 2), (3, 4, 2) is perpe...

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  4. Find the equation of the line in vector and in cartesian form that pa...

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  5. Find the equation of the line which passes through the point (1, 2, 3...

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  6. The cartesian equation of a line is (x-5)/3=(y+4)/7=(z-6)/2. Write i...

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  7. Find the cartesian equation of the line which passes through the poin...

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  8. Find the vector and the cartesian equations of the line that passes t...

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  9. Find the vector and the cartesian equations of the lines that passes ...

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  10. Find the values of p so that the lines (1-x)/3=(7y-14)/(2p)=(z-3)/2an...

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  11. Show that the lines (x-5)/7=(y+2)/(-5)=z/1and x/1=y/2=z/3are perpendi...

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  12. Find the angle between the following pairs of lines:(i) vec r=2 hat i...

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  13. Find the angle between the following pair of lines: (i) (x-2)/2=(y-1)...

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  14. Find the shortest distance between the lines whose vector equations a...

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  15. Find the shortest distance between the lines whose vector equations a...

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  16. Find the shortest distance between the lines vec r=( hat i+2 hat j+ ...

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  17. Find the shortest distance between the lines(x+1)/7=(y+1)/(-6)=(z+1)/...

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