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Find the perpendicular distance from the point (1,2,3) to the line : `vecr=6hati+7hatj+7hatk+lambda(3hati+2hatj-2hatk)`

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Find the coordinates of the foot of the perpendicular and the length of the perpendicular drawn from the point P(5,4,2) to the line vecr=(-hati+hatj+hatk)+lambda(2hati+hatj-hatk) . Also find the image of P in this line.

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

Find the equation of the line passing through the point (1,2,-3) and perpendicular to the lines : vecr=(2hati-hatj-hatk)+lambda(2hati-hatj-3hatk) and vecr=(3hati-hatj-2hatk)+mu(hati+hatj+hatk)

Find the equation of the line passing through the point (1,-2,3) and perpendicular to the lines : vecr=(hati-2hatj+hatk)+lambda(hati+hatj+hatk) and vecr=(hati-hatj+2hatk)+mu(3hati-2hatj-5hatk)

Find the shortest distance between each of the following pair of lines: vecr=3hati+5hatj+7hatk+lambda(hati-2hatj+7hatk) and vecr=-hati-hatj-hatk+mu(7hati-6hatj+hatk) .

Find the equation of the line perpendicular to the lines : vecr=(3hati+2hatj-4hatk)+lambda(hati+2hatj-2hatk) and vecr=(5hatj-2hatk)+mu(3hati+2hatj+6hatk) and passing through the point (1,1,1)

Find the equation of the line passing through the point (2, -1, 3) and perpendicular to the lines : vecr=(hati-hatj+hatk)+lambda(2hati+hatj-3hatk) and vecr=(hati+hatj-hatk)+mu(hati+hatj+hatk)

Find the distance of the point (2,12,5) from the point of intersection of the line: vecr=2hati-4hatj+2hatk+lambda(3hati+4hatj+2hatk) and the plane vecr*(hati-2hatj+hatk)=0 .

Find the shortest distance between the lines given by the. equations : vecr=(hati-hatj+2hatk)+lambda(2hati-hatj-4hatk) and vecr=(2hati-4hatj+hatk)+mu(3hati+hatj-5hatk) .

Find the vector and Cartesian form of the equation of the plane passing through the point (1, 2, -4) and parallel to the lines vecr=hati+2hatj-4hatk+lamda(2hati+3hatj+6hatk) and vecr=hati-3hatj+5hatk+mu(hati+hatj-hatk) .

MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. Find the perpendicular distance of the point (1,0,0) from the line : (...

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  2. Find the length of the perpendicular from the point (1,2,3) to the lin...

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  3. Find the perpendicular distance from the point (1,2,3) to the line : v...

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  4. Find the image of the point (2,-1,5) in the line (x-11)/(10)=(y+2)/(-4...

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  5. Find the foot of the perpendicular from the point (0,2,3) on the line ...

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  6. Find the coordinates of the foot of the perpendicular drawn from point...

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  7. A(1,0,4), B(0,-11,3), C(2,-3,1) are three points and D is the foot of ...

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  8. The perpendicular distance of a corner of a unit cube from a diagonal ...

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  9. Find the image of the point (2,0,1) in the line (x-3)/(1)=(y+2)/(-2)...

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  10. Find the image of the point (1, 2, 3) in the line (x-6)/(3)=(y-7)/(2)=...

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  11. Find the image of the point A(-1,8,4) in the line joining the points B...

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  12. Let the point P(5,9,3) lie on the top of Qutub Minar, Delhi.Find the i...

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  13. Find the foot and hence the length of the perpendicular from the point...

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  14. Find the length and foot of perpendicular drawn from the point (2,-1,3...

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  15. Find the equations of the perpendicular drawn from the point (2,4,-1) ...

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  16. Find the length of perpendicular from point (2, 3, 4) to the (4-x)/(2...

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  17. Find the equations of the perpendicular from the point (3,-1,11,) to t...

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  18. A line passing through the point A with position vector veca=4hati+2ha...

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  19. 1 Find the shortest distance between the lines l1 and l2 whose vector ...

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  20. Find the shortest distance between two lines whose vector equations ar...

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