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What is the shortest distance between two intersecting lines?

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Find the shortest distance between two lines whose vector equations are : vecr=hati-7hatj-2hatk+lambda(hati+3hatj+2hatk) and vecr=-3hati+4hatj-2hatk+mu(-hati+2hatj+hatk)

Find the shortest distance between two lines whose vector equations are : vecr=hati+2hatj+hatk+lambda(hati+hatj+hatk) and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk)

Find the shortest distance between the two given lines vecr=6hati+2hatj+2hatk+lambda(hati-2hatj+2hatk) and vecr=4hati-hatk+mu(3hati-2hatj-2hatk)

Find the shortest distance between the two given lines vecr=2hati+3hatj+4hatk+lambda(2hati-hatj+hatk) and vecr=3hati-2hatj-hatk+mu(3hati+2hatj-4hatk)

Find the shortest distance between two lines whose vector equations are : vecr=3hati+8hatj+3hatk+lambda(3hati-hatj+hatk) and vecr=-3hati-7hatj+6hatk+mu(-3hati+2hatj+4hatk)

Find the S.D (shortest distance) between the two given lines vecr=hati+hatj+lambda(2hati-hatj+hatk) and vecr=2hati+hatj-hatk+mu(3hati-5hatj+2hatk)

Find the shortest distance and the equation of the shortest distance between the following two lines: vecr=(-hati+hatj+9hatk)+lambda(2hati+hatj-3hatk) and vecr=(3hati-15hatj+9hatk)+mu(2hati-7hatj+5hatk)

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. What is the locus of the equations x^2+y^2+z^2=0?

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  2. Write the direction cosines of the Y-axis.

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  3. What is the shortest distance between two intersecting lines?

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  4. Direction cosines of hat i are ‘

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  5. Write down direction cosines of the line (1-x)/1=(y-2)/1=(z-3)/1.

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  6. What is the angle between the planes x+y=0 and z=0.

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  7. Name the surface represented by the equation ax+by+cz+d=0, where a^2+b...

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  8. Write the attitude numbers of the plane 2x-3y+4z-13=0.

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  9. Find p if the planes 2x+3y+6z-13=0 and 6x+py-3z=0 are at right angles.

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  10. Find lambda if the lines x/6=y/2=z/-3 and x/p=y/-6=z/2 are at right an...

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  11. Find the intercepts of the plane 2x-3y+4z-24=0 on the cooridnate axes.

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  12. Find the distance of the plane x+y+z-sqrt3=0 from the origin.

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  13. Does the line x=y=0 lie in the plane z=0.

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  14. Name the surface represented by the equation 2x-3y=0.

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  15. Find the distance between the point (2,3,6) and (0,0,0).

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  16. Write down the coordinates of the mid point of the segment joining the...

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  17. If the direction ratios of a line <2,-1,-2> find the direction cosines...

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  18. find the vector equations of the line which is parallel to the vector ...

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  19. Find the direction cosines of the line passing through the points P(2,...

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  20. If a line makes an angles of 30^@, 60^@, 90^@ with the positive direct...

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