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Find the value of a so that the four poi...

Find the value of a so that the four points with position vectors `-hatj+hatk,2hati-hatj-hatk,hati+lambdahatj+hatk` and `3hatj+3hatk` are co-plannar.

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The correct Answer is:
`lambda=1`
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KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-PRACTICE WORK
  1. Find the cartesian equation of the plane through the point (2,-1, 1) a...

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  2. Find the vector equation of the plane passing through the points (1, -...

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  3. Find the value of a so that the four points with position vectors -hat...

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  4. A plane meets the co-ordinate axes at A, B and C such that the centroi...

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  5. Show that the plane through (1, 1, 1), (1,-1, 1) and (-7, 3, -5) is pe...

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  6. The foot of perpendicular from the origin to the plane is (4, -2, -5) ...

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  7. Find the equation of the plane passing through the point (-1,2, 1) and...

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  8. Find the equation of the plane containing the line of intersection of ...

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  9. Find the equation of the plane through the line of intersection of vec...

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  10. Find the equation of the plane passing through the intersection of the...

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  11. Find the cartesian equation of the plane| through the intersection of ...

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  12. Find the equation of the plane passing through the intersection of the...

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  13. In the following cases, determine whether the given planes are paralle...

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  14. If the planes vecr.(hati+2hatj-3hatk)=7 and vecr.(lambdahati+2hatj-7ha...

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  15. Find the distance of the point (2, 1, 0) from the plane 2x + y + 2z + ...

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

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  17. Find the distance between the parallel planes x + y - z + 4 = 0 and x ...

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  18. Find the distance between the parallel planes vecr.(2hati-3hatj+6hatk...

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

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

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