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If the points (1, 1, p) and (-3, 0, 1) b...

If the points (1, 1, p) and (-3, 0, 1) be equidistant from the plane `vecr.(3hati+4hatj-12hatk)+13=0` then find the value of p.

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The correct Answer is:
`therefore p=1` or `p=7/3`
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If the points (1, 1, lambda ) and (-3, 0, 1) be equidistant from the plane vecr.(3hati+4hatj-12hatk)+13=0 find the value of lambda .

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If p=7hati-2hatj+3hatk and q=3hati+hatj+5hatk , then find the the magnitude of p-2q.

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

Find the distance of the point (-1, -5, -10) from the point of intersection of the line vecr=2hati-hatj+2hatk+lambda(3hati+4hatj+2hatk) and the plane vecr.(hati-hatj+hatk)=5

Find the equation of the plane passing through (a, b, c) and parallel to the plane vecr.(hati+hatj+hatk)=2 .

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

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes vecr.(hati-hatj+2hatk)=5 and vecr.(3hati+hatj+hatk)=6

Find the vector and cartesian equations of the planes : (a) that passes through the point (1, 0, -2) and the normal to the plane is hati+hatj-hatk . (b) that passes through the point (1,4, 6) and the normal vector to the plane is hati-2hatj+hatk .

KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-MISCELLANEOUS EXERCISE-11
  1. Find the equation of a line parallel to X- axis and passing through th...

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  2. If the coordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7), (...

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  3. If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/(2) and (x-1)/(3k)=(y-1)/(1)=...

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  4. Find the vector equation of the line passing through (1, 2, 3) and per...

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  5. Find the equation of the plane passing through (a, b, c) and parallel ...

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  6. Find the shortest distance between lines vecr=6hati+2hatj+2hatk+la...

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  7. Find the coordinates of the point where the line through (5, 1, 6) and...

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  8. Find the coordinates of the point where the line through (5, 1, 6) and...

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  9. Find the coordinates of the point where the line through (3,--4,-5) an...

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  10. Find the equation of the plane passing through the point (-1, 3, 2) an...

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  11. If the points (1, 1, p) and (-3, 0, 1) be equidistant from the plane v...

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

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  13. If O be the origin and the coordinates of P be (1, 2, - 3), then find ...

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  14. Find the equation of the plane which contains the line of intersection...

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  15. Find the distance of the point (-1, -5, -10) from the point of interse...

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  16. Find the vector equation of the line passing through (1, 2, 3) and par...

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  17. Find the vector equation of the line passing through the point (1, 2, ...

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  18. Prove that if a plane has the intercepts a, b, c and is at a distance ...

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  19. Distance between the two planes : 2x + 3y + 4z = 4 and 4x + 6y + 8z = ...

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  20. The planes : 2x – y + 4z = 5 and 5x – 2.5 y + 10 z = 6 are

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