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Consider the line vecr = (hati+2hatj-hat...

Consider the line `vecr = (hati+2hatj-hatk)+lambda(2hati+hatj+4hatk)` and the plane `vecr .(hati-6hatj+hatk)+12=0`.Prove that the line lies on the plane.

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Consider the line vecr = (hati+2hatj-hatk)+lambda(2hati+hatj+4hatk) and the plane vecr . (hati-6hatj+hatk)+12=0 . Find a vector parallel to the line and a vector normal to the plane.

The angle between the straight line r=(hati+2hatj+hatk)+lambda(hati-hatj+hatk) and the plane r.(2hati-hatj+hatk)=4 is

Consider the straight lines vecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk )and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk ) Show that these lines are not coplanar.

Consider the vectors veca=hati+2hatj-3hatk and vecb=4hati-hatj-2hatk . Find veca.vecb

A N EXCEL PUBLICATION-THREE DIMENSTIONAL GEOMETRY-QUESTION BANK
  1. Consider the line (x-1)/2 = (y-2)/-3=(z+5)/4 and the plane 2x+4y-z=3. ...

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  2. Consider the line vecr = (hati+2hatj-hatk)+lambda(2hati+hatj+4hatk) an...

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  3. Consider the line vecr = (hati+2hatj-hatk)+lambda(2hati+hatj+4hatk) an...

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  4. Determine the direction cosines of the normal to the plane and the dis...

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  5. Determine the direction cosines of the normal to the plane and the dis...

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  6. Determine the direction cosines of the normal to the plane and the dis...

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  7. Determine the direction cosines of the normal to the plane and the d...

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  8. Find the vector equation of a plane which is at a distance of 7 units ...

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  9. Find the cartesian equation fo the following planes. vecr.(hati+hatj-h...

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  10. Find the cartesian equation fo the following planes.vecr.(2hati+3hatj-...

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  11. Find the cartesian equation fo the following planes. vecr.[(s-2t)hati+...

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  12. Find the co-ordinates of the foot of the perpendicular drawn from th...

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  13. In the following cases, find the co-ordinates of the foot of the perpe...

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  14. Find the co-ordinates of the foot of the perpendicular drawn from th...

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  15. Find the co-ordinates of the foot of the perpendicular drawn from the ...

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  16. Find the vector and cartesian equations of the plane that passes throu...

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  17. Find the vector and cartesian equations of the plane that passes throu...

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  18. Find the equation of the planes that pass through the points.. (1, 1,...

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  19. Find the equation of the planes that pass through the points... (1, ...

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  20. Find the intercepts cut off by the plane 2x + y - z = 5

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