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Find the length of the perpendicular drawn from point `(2,3,4)` to line `(4-x)/2=y/6=(1-z)/3dot`

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Column I, Column II The coordinates of a point on the line x=4y+5,z=3y-6 at a distance 3 from the point (5,3,-6) is/are, p. (-1,-2,0) The plane containing the lines (x-2)/3=(y+2)/5=(z+5)/7 and parallel to hat i+4 hat j+7 hat k has the point, q. (5,0,-6) A line passes through two points A(2-3,-1)a n dB(8,-1,2)dot The coordinates of a point on this line nearer to the origin and at a distance of 14 units from A is/are, r. (2,5,7) The coordinates of the foot of the perpendicular from the point (3,-1,11) on the line x/2=(y-2)/3=(z-3)/4 is/are, s. (14 ,15)

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CENGAGE PUBLICATION-THREE DIMENSIONAL GEOMETRY-All Questions
  1. Find the condition if lines x=a y+b ,z=c y+da n dx=a^(prime)y+b^(prime...

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  2. Find the acute angle between the lines (x-1)/l=(y+1)/m=1/na n d=(x+...

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  3. Find the length of the perpendicular drawn from point (2,3,4) to li...

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  4. Find the coordinates of the foot of the perpendicular drawn from po...

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  5. Find the vector equation of the line passing through (1,2,3) and par...

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  6. The value of m for which the straight line 3x-2y+z+3 = 0=4x-3y+4z+1. i...

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  7. Show that the lines (x-a+d)/(alpha-delta)=(y-a)/alpha=(z-a-d)/(alph...

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  8. Find the equation of line x+y-z-3=0=2x+3y+z+4 in symmetric form. Find ...

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  9. Find the vector equation of line passing through the point (1,2,-4)...

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  10. Find the vector equation of line passing through A(3,4-7)a n dB(1,-...

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  11. Find Cartesian and vector equation of the line which passes through...

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  12. Find the equation of a line which passes through the point (2,3,4) ...

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  13. Find the points where line (x-1)/2=(y+2)/(-1)=z/1 intersects x y ,y za...

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  14. A mirror and source of light are situated at the origin O and a point ...

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  15. The Cartesian equation of a line is (x-3)/2=(y+1)/(-2)=(z-3)/5 . Fi...

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  16. The Cartesian equations of a line are 6x-2=3y+1=2z-2. Find its dire...

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  17. A line passes through the point with position vector 2 hat i-3 hat ...

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  18. Find the plane of the intersection of x^2+y^2+z^2+2x+2y+2=0 and 4x^2...

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  19. Let l1a n dl2 be the two skew lines. If P ,Q are two distinct points o...

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  20. If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/(-2) and (x-1)/(3k)=(y-5)/1=(...

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