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

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

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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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Show that the points P(hati-hatj+3hatk) and Q(3hati+3hatj+3hatk) are equidistant from the plane vecr.(5hati+2hatj-7hatk)+9=0 and lie on opposite sides of it.

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Find the point, where the line joining the points (1,3,4) and (-3,5,2) intersects the plane vecr*(2hati+hatj+hatk)+3=0 . Is the point equaidistant from the gien points?

Find a unit vector normal to the plane : vecr*(2hati-3hatj+6hatk)+14=0 .

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Find the angle between the line joing (3,-4,-2) and(12, 2, 0) and the plane vecr*(hati+hatj+hatk)=4

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MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. Find the coordinates of the point where the line through (3, – 4, – 5)...

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

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

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

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

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

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  7. Find the distance of the point (-1 , -5 , -10) from the point of inter...

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

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  9. Find the vector equation of the line passing through the point (1,2,-4...

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  10. Prove that if a plane has intercepts a,b,c and is at a distance of p u...

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  11. Find the Distance between the two planes 2x+3y+4z=4 and 4x+6y+8z=12

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

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  13. The x, co-ordinate of a point on the line joining the points Q (2, 2, ...

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  14. Find the distance of the point (-1 , -5 , -10) from the point of inter...

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  15. Find the equation of a plane which is at a distance 3sqrt3 units from ...

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  16. Find the equation of the two lines through the origin which intersect ...

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  17. The plane ax+by=0 is rotated through an angle alpha about its line of ...

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  18. Show that the sequence t n defined by t n = 3 n + 1 is an AP.

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  19. Prove that the lines, whose direction cosines are given by al+bm+cn=0,...

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  20. Prove that the lines, whose direction cosines are given by al+bm+cn=0,...

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