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Find the vector and cartesian equations of the line passing through the point (2, 1, 3) and perpendicular to the lines `(x-1)/(1) = (y-2)/(2) = (z-3)/(3)` and `(x)/(-3) = (y)/(2) = (z)/(5)`.

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The correct Answer is:
`r = 2hat(i) + hat(j) + 3hat(k) + lambda (2hat(i) - 7hat(j) + 4hat(k))`
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Find the equations of the plane passing through the point (2, 1, 3) and perpendicular to the lines (x-1)/1=(y-2)/2=(z-3)/3 .

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ARIHANT PUBLICATION-THREE-DIMENSIONAL GEOMETRY-Part III Questions For Practice ( Lines in Space) Short Answer Type Questions
  1. Evaluate the following integrals : int(x^(2)/sinx^(3))dx

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  2. Find the co-ordinates of the point where the perpendicular from the or...

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  3. Show that the lines at (5-x)/(-4) = (y-7)/(4) = (z+3)/(-5) and (x-8)/(...

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  4. Find the points on the line (x+2)/(3) = (y+1)/(2) = (z-3)/(2)  at a d...

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  5. The cartesian equations of a line is 6x - 2 = 3y + 1 = 2z - 2. Find th...

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  6. Show that the line through the points (1 - 1,2), (3, 4,-2) is perpendi...

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  7. Find the equation of a linę passing through the point (1, 2 - 4) and p...

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  8. Find the vector and cartesian equations of the line passing through th...

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  9. Find the vector and cartesian equation of a line through the point (1,...

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  10. Find the foot of the perpendicular from (1, 2 , - 3) to the line (x+1)...

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  11. Find the shortest distance between the following lines vecr = 2hat(i) ...

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  12. Find the shortest distance between the lines  (x-3)/(1) = (y - 5)/(-2)...

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  13. By computing shortest distance, determine whether the following pair o...

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  14. Show that the (x-1)/(3) = (y+1)/(2) = (z-1)/(5) and (x+2)/(4) = (y-1)/...

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  15. Find the equation of the plane passing through the line x = y = z and ...

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  16. Find the image of the point (-2,0,3) with respect to the plane y = 3.

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  17. Find the value of r, if the line  (x-1)/(1) = (y+2)/(3) = (z-1)/(-1) =...

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  18. Determine the symmetric form of the equation to the line of intersecti...

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  19. Evaluate the following integrals : int(sinx+x^(2))dx

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