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The number of planes that are equidistan...

The number of planes that are equidistant from four non-coplanar points is

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Let n be the number of points having rational coordinates equidistant from the point (0,sqrt3) , then

A point P moves in such a way that the ratio of its distance from two coplanar points is always a fixed number (!=1) . Then, identify the locus of the point.

A & B are two pts (0,2,3) and (2,-2,1) respectively find the locus of a point P such that it is equidistant from the given points

Find the equation of the set of points which are equidistant from the points (1,2,3) and (3,2,-1)

Prove that in a G.P. of finite number of terms the product of any terms equidistant from the beginning and the end is constant and is equal to the product of the first and last terms.

Prove that in an A.P. of finite number of terms the sum of any two terms equidistant from the beginning and the end is equal to the sum of the first and last terms.

Some points are plotted on a plane such that any three of them are non collinear. Each point is joined with all remaining points by line segments. Find the number of points if the number of line segments are 10.

Find the coordinates of the point equidistant from the four points ( 2 ,1 , 2 ) ,( -1 , 1, 3) ,( 0 , 5 , 6) and (3 , 2 , 2) .

Find the coordinates of the point lies on the plane YOZ which is equidistant from the points A(1,-1,0),B(2,1,2) and C(3,2,-1).

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CENGAGE PUBLICATION-THREE DIMENSIONAL GEOMETRY-All Questions
  1. The coordinates of the point P on the line vec r=( hat i+ hat j+ h...

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  2. The ratio in which the line segment joining the points whose positio...

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  3. The number of planes that are equidistant from four non-coplanar point...

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  4. In a three-dimensional coordinate system, P ,Q , and Rare images of a...

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  5. A plane passing through (1,1,1) cuts positive direction of coordinates...

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  6. If lines x=y=za n dx=y/2=z/3 and third line passing through (1,1,1) fo...

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  7. The point of intersection of the line passing through (0,0,1) and ...

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  8. Shortest distance between the lines (x-1)/1=(y-1)/1=(z-1)/1a n d(x-...

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  9. Distance of point P( vec p) from the plane vec rdot vec n=0 is a. | v...

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  10. The reflection of the point vec a in the plane vec rdot vec n=q is...

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  11. Line vec r= vec a+lambda vec b will not meet the plane vec rdot vec ...

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  12. If a line makes an angle of pi/4 with the positive direction of ea...

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  13. Find the equation of the plane containing the lines 2x-y+z-3=0,3x+y+z=...

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  14. A plane which prependicular totwo planes 2x-2y+z=0and x-y+2z=4 passes ...

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  15. Let P(3,2,6) be a point in space and Q be a point on line vec r=( hat...

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  16. If the lines (x-1)/2=(y+1)/3=(z-1)/4 and (x-3)/1=(y-k)/2=z/1 intersec...

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  17. Consider a set of point R in which is at a distance of 2 units from t...

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  18. Consider the lines L1:(x-1)/2=y/(-1)=(z+3)/1,L2:(x-4)/1=(y+3)/1=(z+3)/...

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  19. Statement 1: A plane passes through the point A(2,1,-3)dot If distan...

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  20. Consider the following linear equations: a x+b y+c z=0 b x+c y+a z=0 c...

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