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Find the values of lambda if the followi...

Find the values of `lambda` if the following of lines perpendicular :
`(1-x)/(3) = (7y-14)/(3lambda)=(z+1)/(2)` and `(7-7x)/(3lambda) = y/1 = (1-z)/(5)`

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`35/6`
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Find the value of 'lambda' so the lines: (1-x)/(3) = (7y -14)/(lambda) = (z-3)/(2) and (7 - 7x)/(3 lambda) = (y -5)/(1 ) = (6 - z)/(5) are at right angles. Also, find whether the lines are ntersecting or not .

Find the value of so that the lines l1: (1-x)/3 = (7y-14)/(2lambda) =(z-3)/2 and l2: (7-7x)/(3lambda) = (y-5)/1 = (6-z)/5 are at right angle. Also find the equation of a line passing through the point (3,2,-4) and parallel to l1.

Find the value of lambda so that the following lines are perpendicular to each other.(x-5)/(5 lambda+2)=(2-y)/(5)=(1-z)/(-1),(x)/(1)=(2y+1)/(4 lambda)=(1-z)/(-3)

Fiind m, if the lines (1-x)/(3)= ( 7y-14)/(2m ) = (z-3) /(2) and ( 7-7x)/(3m) = (y-5)/(1) = (6-z)/(5) are at right angles.

(i) Find the value of 'p' so that the lines : l_(1) : (1 - x)/(3) = (7y -14)/(2p) = (z - 3)/(2) and l_(2) : (7 -7x)/(3p) = (y - 5)/(1) = (6 - z)/(5) are at right angles. Also, find the equations of the line passing through (3,2, -4) and parallel to line l_(1) . (ii) Find 'k' so that the lines : (x - 3)/(2) = (y + 1)/(3 ) = (z - 2)/(2k) and (x + 2)/(1) = (4 -y)/(k) = (z + 5)/(1) are perpendicular to each other.

Write the value of lambda for which the lines (x-3)/(-3)=(y+2)/(2lambda)=(z+4)/2a n d(x+1)/(3lambda)=(y-2)/1=(z+6)/(-5) are perpendicular to each other.

Find the directions ratios of the line perpendicular to the lines (x-7)/(2) = ( y+ 7)/(-3) =(z-6)/(1) and (x+5)/(1) = (y+3)/(2)= (z-6)/(-2)

Find the values p so that line (1-x)/(3)=(7y-14)/(2p)=(z-3)/(2) and (7-7x)/(3p)=(y-5)/(1)=(6-z)/(5) are at right angles.

The value of lambda for which the two lines (x-1)/(4)=(y-2)/(1)=(z)/(1)delta(x+7)/(lambda)=(y)/(lambda-5)=(z-lambda)/(2) are coplaner

Find the value of lambda such that the lines (x-2)/6=(y-1)/lambda=(z+5)/(-4) is perpendicular to the plane 3x-y-2z=7.

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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