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Find the image of the point (3hati-hatj+...

Find the image of the point `(3hati-hatj+11hatk)` in the line `vecr = 2 hatj + 3hatk+lambda(2hati+3hatj+4hatk)`.

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The correct Answer is:
`hati+11hatj+3hatk`
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Find the co-ordinates of the foot of perpendicular and length of perpendicular drawn from point (hati+6hatj+3hatk) to the line vecr = hatj+2hatk+lambda(hati+2hatj+3hatk) .

Prove that the plane vecr*(hati+2hatj-hatk)=3 contains the line vecr=hati+hatj+lamda(2hati+hatj+4hatk).

The position vector of the foot of the perpendicular draw from the point 2hati-hatj+5hatk to the line vecr=(11hati-2hatj-8hatk)+lamda(10hati-4hatj-11hatk) is

Find the points of intersection of the line vecr = 2hati - hatj + 2hatk + lambda(3hati + 4hatj + 2hatk) and the plane vecr.(hati - hatj + hatk) = 5

Find the shortest distance between the lines vecr = 2hati - hatj + hatk + lambda(3hati - 2hatj + 5hatk), vecr = 3hati + 2hatj - 4hatk + mu(4hati - hatj + 3hatk)

Find the equation of the line through the point hati+hatj-3hatk and perpendicular to the lines vecr=2hati-3hatj+s(2hati+hatj-3hatk)andvecr=3hati-5hatk+t(hati+hatj+hatk)

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

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

Find the angle between the following lines and the planes : (i) line vecr=(hati+2hatj-hatk)+lambda(hati-hatj+hatk) and planes vecr.(2hati-hatj+hatk) = 4 . (ii) line vecr = (2hati+3hatj+9hatk)+lambda(2hati+3hatj+4hatk) and plane vecr.(hati+hatj+hatk) =5 . (iii) line (x+1)/(3) = y/2 = z/4 and plane 2x+y-3z=5 . (iv) line (x-3)/(9) = (y+4)/(6) = (z+2)/(2) and plane 3x-y+z=0 .

NAGEEN PRAKASHAN-THREE-DIMENSIONAL GEOMETRY -Exercise 11 B
  1. The cartesian equation of a line is 6x+1=3y-2 = 3-2x. Find its directi...

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  2. Find the angle between the following pairs of lines (i) veci=3hati+2...

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  3. (i) Show that the line (x+3)/(2) = (y+1)/(-1) = (z+3)/(3) and (x)/(5) ...

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  4. Find the values of lambda if the following of lines perpendicular : ...

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  5. Show that the following pairs of lines intersect. Also find their poin...

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  6. Show that the lines (x-1)/(1) = (y-2)/(-1) = (z-1)/(1) and (x-1)/(1-...

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  7. Show that the lines vecr= hati+hatj-hatk+lambda(3hati-hatj) and vecr =...

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  8. Find the co-ordinates of that point at which the lines joining the poi...

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  9. Find the co-ordinates of that point at which the line joining the poin...

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  10. Find the co-ordinates of a point at which the line (x+1)/(2) = (y-3)/(...

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  11. Find the co-ordinates of a point at which the line (x+1)/(2) = (y-1)/(...

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  12. Find the co-ordiantes of the foot of perpendicular drawn from the poi...

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

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  14. Find the co-ordinates of the foot of perpendicular and length of perp...

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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 image of the point (0,2,3) in the line (x+3)/(5)= (y-1)/(2) =...

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  17. Find the image of the point (3hati-hatj+11hatk) in the line vecr = 2 h...

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  18. Find the shortest distance between the following lines : (i) vecr=4h...

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  19. Find the co-ordinates of the point at a distance of sqrt(5)units from ...

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  20. Find the co-ordinates of the point at a distance of sqrt(14) from the ...

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