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If the distance of the plane x - y + z +...

If the distance of the plane x - y + z + `lambda` = 0 from the point (1, 1, 1) is `d_1` and the distance of this point from the origin is `d_2` and `d_2d_2` = 5 then find the value of `lambda`.

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The correct Answer is:
`lambda=4`
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KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-PRACTICE WORK
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  2. Find the distance between the parallel planes vecr.(2hati-3hatj+6hatk...

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  3. If the distance of the plane x - y + z + lambda = 0 from the point (1,...

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  4. The direction cosines of two lines are 1, -2,-2 and 0, 2, 1. Find the ...

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  5. The direction cosines of two lines are given by the following equation...

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  6. Show that the line passing through the points (4, 7, 8) and (2, 3, 4) ...

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  7. Show that the line passing through (1, -1, 2) and (3, 4, -2) is perpen...

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  8. Find the angle between the lines (5-x)/(-2)=(y+3)/(1)=(1-z)/(3) and x/...

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  9. Show that the lines (x-5)/(7)=(y+2)/(-5)=z/1 and x/1=y/2=z/3 are perpe...

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

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  11. Find the co-ordinates of the point where the line through A(3, 4, 1) a...

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

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

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  14. Find the image of the point (3, 5, 3) with respect to the line x/1=(y-...

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  15. Find the equation of the plane passing through the points (1, 2, 3) an...

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  16. Find the equation of the plane passing through the line of intersectio...

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  17. Find the equation of the plane passing through the point (3, 4, -1) an...

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  18. Find the equation of the plane passing through the line of intersectio...

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  19. If the points (1, 1, lambda) and (-3, 0, 1) be equidistant from the pl...

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  20. Find the vector equation of the plane containing the lines vecr=(hati+...

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