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Find the direction cosines of perpendicu...

Find the direction cosines of perpendicular from the origin to the plane `vecr.(6hati-3hatj-2hatk)+1=0`.

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The correct Answer is:
`6/7,(-3)/(7),(-2)/(7)`
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Find the direction cosines of the unit vector perpendicular to the plane vecr.(6hati-3hatj-2hatk)+1=0 passing through the origin.

Find the direction cosines of the vector hati+2hatj+3hatk .

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane vecr.(hati+2hatj-5hatk)+9=0

Find the cartesian equation of the plane| through the intersection of the planes vecr.(2hati+6hatj)+12=0 and vecr.(3hati-hatj+4hatk)=0 which are at a unit distance from the origin.

Find the distance of a point (2, 5, -3) from the plane vecr.(6hati-3hatj+2hatk)=4

Find the equation of the plane passing through the line of intersection of the planes vecr.(hati+3hatj-hatk)=0 and vecr.(hatj+2hatk)=0 and also passing through the point 2hati+hatj-hatk .

Find the vector equation of the plane passing through the intersection of the planes vecr.(hati+hatj+hatk)=6 and vecr.(2hati+3hatj+4hatk)=-5 and the points (1,1,1).

Find the direction cosines of the resultant of the vectors (hati+hatj+hatk),(-hati+hatj+hatk),(hati-hatj+hatk) and (hati+hatj-hatk) .

Find the image of the point (1, 3, 4) in the plane vecr.(2hati-hatj+hatk)+3=0

Find the equation of the plane passing through the line of intersection of the planes vecr.(hati+hatj+hatk)=1 and vecr.(2hati+3hatj-hatk)+4=0 and parallel to X- axis.

KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-PRACTICE WORK
  1. Find the shortest distance between the lines (x-1)/(2)=(y-2)/(3)=(...

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  2. Find the shortest distance between the lines vecr=(lambda-1)hati+(...

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  3. Find the direction cosines of perpendicular from the origin to the pla...

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  4. Find the vector equation of a plane which is at a distance 11 units fr...

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  5. Find the vector equation of the plane vecr=hati-hatj+lambda(hati+hatj+...

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  6. Find the cartesian equation of the plane through the point (2,-1, 1) a...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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