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Find the value of lambda such that the l...

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

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The correct Answer is:
`lambda=-2`
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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.

Find the value of lambda for which the line (x-1)/2=(y-1)/3=(z-1)/lambda is parallel to the plane vecr.(2hati+3hatj+4hatk)=4 .

Find the value of lambda for which the planes x-4y+lambdaz+3=0 and 2x+2y+3z=5 are perpendicular to each other.

Find the value of lambda for which the planes 2x-4y+3z=7 and x+2y+lambdaz=18 are perpendicular to each other.

Prove that the plane 2x+3y-4z=9 is perpendicular to each of the planes x+2y+2z-7=0 and 5x+6y+7z=23 .

(i) Find the equation of the plane passing through (1,-1,2) and perpendicular to the planes : 2 x + 3y - 2z = 5 , x + 2y - 3z = 8 . (ii) find the equation of the plane passing through the point (1,1,-1) and perpendicular to each of the planes : x + 2y + 3z - 7 = 0 and 2x - 3y + 4z = 0 . (iii) Find the equation of the plane passing through the point (-1,-1,2) and perpendicular to the planes : 3x + 2y - 3z = 1 and 5x - 4y + z = 5.

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 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)

Determine the value of lambda for which the following plane are perpendicular to each other. 3x-6y-2z=7\ a n d\ 2x+y-lambdaz=5

RS AGGARWAL-THE PLANE-Exercise 28J
  1. The equation of a plane parallel to x-axis is

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  2. Write the intercept cut off by the plane 2x+y-z=5 on x-a xi sdot

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  3. Write the intercepts made by the plane 4x-3y+2z=12 on the coordinate a...

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  4. Reduce the equation 2x-3y+5z+4=0 to intercept form and find the interc...

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  5. Find the equation of a plane passing through the points A(a,0,0), B(0,...

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  6. Write the value of k for which the planes 2x-5y+kz=4 and x+2y-z=6 are ...

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  7. Find the angle between the planes 2x + y - 2z = 5 and 3x - 6y - 2z = 7...

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  8. Find the angle between the planes vecr.(hati+hatj)=1 and vecr.(hati+ha...

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  9. Find the angle between the planes vecr.(3hati-4hatj+5hatk)=0 and vecr....

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  10. Find the angle between the line (x+1)/2=y/3=(z-3)/6and the plane 10 ...

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  11. Find the angle between the line vecr=(hati+hatj-2hatk)+lambda(hati-hat...

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  12. Find the value of lambda such that the line (x-2)/6=(y-1)/lambda=(z+5)...

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  13. Find the equation of the plane passing through (a,b,c) and paralle tot...

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  14. Find the length of the perpendicular drawn from the origin to the p...

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  15. Find the direction cosines of the perpendicular from the origin to th...

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  16. Show that the line vecr=(4hati-7hatk)+lambda(4hati-2hatj+3hatk) is par...

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  17. Find the length of perpendicular from the origin to the plane vecr.(2h...

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  18. Find the value of lambda for which the line (x-1)/2=(y-1)/3=(z-1)/lamb...

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  19. Write the angle between the line (x-1)/2=(y-2)/1=(z+3)/-2 and the plan...

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  20. Write the equation of a plane passing through the point (2,-1,0) and p...

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