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Find the angle between the line vecr=hat...

Find the angle between the line `vecr=hati+2hatj-hatk+lamda(hati-hatj+hatk)` and the plane `vecr*(2hati-hatj+hatk)=4`.

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The correct Answer is:
(i) `sin^(-1)((2sqrt(2))/(3))`, (ii) `sin^(-1)((3sqrt(3))/(sqrt(29)))`, (iii) `sin^(-1)((-4)/(sqrt(406)))` , (iv) `sin^(-1)((23)/(11sqrt(11)))`
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Find the distance of the point (-1,-5,-10) from the point of the intersection of the line vecr = 2hati-2hatk+lambda(3hati+4hatj+2hatk) and the plane vecr.(hati-hatj+hatk) = 5 .

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NAGEEN PRAKASHAN ENGLISH-THREE-DIMENSIONAL GEOMETRY -Exercise 11 E
  1. Find the angle between the line vecr=hati+2hatj-hatk+lamda(hati-hatj+h...

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  2. Find the value of 'm' for which the line vecr= (hati+2hatj-hatk)+la...

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  3. Find the value of 'm' for which the line vecr = hati+lambda(2hati-mhat...

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  4. Find the equation of a plane passing through the points (0,0,0) and (3...

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  5. Find the equation of the plane through (2, 3, -4) and (1, -1, 3) and ...

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  6. Find the equation of a line passing through the point (1,2,3) and perp...

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  7. The equation of the line passing through (1, 2, 3) and parallel to the...

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  8. Find the perpendicular distance from the point (2hati-hatj+4hatk) to t...

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  9. Find the perpendicular distance from the point (2hati+hatj-hatk) to th...

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  10. Find the distance of the point (21,0) from the plane 2x+y+2z+5=0.

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  11. Find the distance of each of the following points from the correspondi...

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  12. If the points (1,1,lamda) and (-3, 0,1) are equidistant from the plan...

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  13. Find the distance between the parallel planes 2x-y+3-4=0\ a n d\ 6x-3y...

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  14. Find the distance between the parallel planes, vec r = dot(2 hat i-3 ...

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  15. Find the equations of the planes parallel to the plane x-2y+2z-3=0 whi...

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  16. Find the length of the foot of the perpendicular from the point (1,1,2...

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  17. Find the coordinates of the foot of the perpendicular from the point ...

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  18. Find the image of the point (1,3,4) in the plane 2x-y+z+3=0.

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  19. Find the image of the point O(0,0,0) in the plane 3x+4y-6z+1=0

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  20. A variable plane which remains at q constant distance 3p from the orig...

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