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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)`

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The correct Answer is:
`(z+2)/(5)`
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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 equation in vector anf cartesian form of the line passing through the point : (2,-1,3) and perpendicular to the lines vecr= (hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vecr= (2hati-hatj-3hatk)+mu(hati+2hatj+2hatk) .

Find the vectoer and cartesian equations of the line through the point (1,2,-4) and perpendicualr of the lines: vecr=(8hati-19hatj+10hatk)+lambda(3hati-16hatj+7hatk) and vecr=(15hati+29hatj+5hatk)+mu(3hati+8hatj-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) .

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes vecr.(hati-hatj+2hatk)=5 and vecr.(3hati+hatj+hatk)=6.

Show that the lines vecr=hati+hatj+hatk+lambda(hati-hatj+hatk) and vecr=4hatj+2hatk+mu(2hati-hatj+3hatk) are coplanar.

Find the angle between the lines vecr=2hati+3hatj-4hatk+lambda(2hati+1hatj+2hatk) and vecr=2hati-5hatk+mu(6hati+3hatj+2hatk)

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

Show that the lines: vecr=(hati+hatj)+lambda(2hati-hatk) and vecr=(2hati-hatj)+mu(hati+hatk-hatk) do not intersect.

ACCURATE PUBLICATION-THREE DIMENSIONAL GEOMETRY-QUESTIONS CARRYING 6 MARKS:
  1. Find the equation of the line passing through the point (2, -1, 3) and...

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  2. Find the direction cosines of a line which makes equal angles with the...

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  3. If the equations of a line AB are (3-x)/1 = (y+2)/-2 = (z-5)/4, then t...

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  4. If the cartesian equations of a line are : (3-x)/5=(y+4)/7=(2z-6)/4, w...

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  5. Find the vector equation of a line passing through (2, -1, 1) and para...

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  6. Find the vector equation of the line through the point (2,-1,-1) and i...

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  7. Find the point on the line (x+2)/(3)=(y+1)/(2)=(z-3)/(2) at a distance...

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  8. Find the coordinates of the point where the line through (3, 4, 1) and...

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  9. Find the coordinates of the point where the line through (3, – 4, – 5)...

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  10. Find the value of p so that the lines : l1:(1-x)/3=(7y-14)/(2p)=(z-3)/...

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

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  12. Find the vector and cartesian equation of the line passing through the...

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  13. Find the equation of the line passing through the point (2, -1, 3) and...

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  14. Find the equation of a line passing through the points A(0, 6, -9) and...

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

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  16. Find the co ordinates of the foot of perpendicular and the length of t...

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  17. Find the shortest distance between the lines : vecr=hati-hatj+lamda(...

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  18. Find the shortest distance between the following lines whose vector eq...

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  19. Find the shortest distance between the lines vecr=hati+2hatj+3hatk+lam...

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  20. Find the shortest distance (S.D.) between the lines : vecr=hatj+lamd...

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  21. Write the vector equation of the following lines and hence find distan...

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