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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. The Cartesian equation of the plane vec r=(1+lambda-mu) hat i+(2-l...

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  2. Find the angle between the lines vec r=3 hat i+2 hat j-4 hat k+lambda...

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  3. Column I, Column II The coordinates of a point on the line x=4y+...

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  4. The distance between the line vec r=(2 hat i-2 hat j+3 hat k)+lambd...

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  5. Find the angle between the line (x-1)/3=(y-1)/2=(z-1)/4 and the pla...

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

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  7. Statement 1: There exist two points on the (x-1)/1=y/(-1)=(z+2)/2 w...

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  8. Statement 1: The shortest distance between the lines x/(-3)=(y-1)/1=(z...

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  9. Find the number of sphere of radius r touching the coordinate axes...

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  10. Find the distance of the z-axis from the image of the point M(2-3,3...

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  11. A line with direction cosines proportional to 1,-5, a n d-2 meets li...

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  12. If the planes vec r ( hat i+ hat j+ hat k)=q1, vec r ( hat i+2a hat j...

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  13. The equation of a line passing through the point vec a parallel to ...

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  14. A straight line L on the xy-plane bisects the angle between O Xa n dO ...

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  15. Statement 1: Vector vec c=-5 hat i+7 hat j+2 hat k is along the bisec...

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  16. The equation of the line x+y+z-1=0, 4x+y-2z+2=0 written in the symmetr...

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  17. The equation of two straight lines are (x-1)/2=(y+3)/1=(z-2)/(-3)a n...

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  18. Statement 1: Lines vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j)a...

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  19. What is the equation of the plane which passes through the z-axis and ...

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  20. Statement 1: let A( vec i+ vec j+ vec k)a n dB( vec i- vec j+ vec k) b...

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