Show that the plane through (1, 1, 1), (...

Show that the plane through (1, 1, 1), (1,-1, 1) and (-7, 3, -5) is perpendicular to XZ-plane.

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Show that the line passing through (1, -1, 2) and (3, 4, -2) is perpendicular to the line passing through the points (0, 3, 2) and (3, 5, 6).

Find the equation of the plane through the points (2, 1,-1) and (-1, 3, 4) and perpendicular to the plane x - 2y + 4z = 10.

Show that the line passing through the points (4, 7, 8) and (2, 3, 4) is parallel to the line passing through the points (-1, -2, 1) and (1, 2, 5).

If the plane passing through (1,1,1),(1,-1,1) and (-1,3,-5) is also passing through (2,k,4) then , k = ..........

Equation of plane passing through the points (2, 2, 1) (9, 3, 6) and perpendicular to the plane 2x+6y+6z-1=0 is

The plane passes through the point (1,-1,-1) and its normal is perpendicular to both the lines (x-1)/(1) = (y+2)/(-2) = (z-4)/(3) and (x-2)/(2) + (y+1)/(-1) = (z+7)/(-1) . The distance of the point (1,3,-7) from thise plane is ..........

Find the equation of the plane passing through the point (-1,2, 1) and perpendicular to the line joining the points (-3, 1, 2) and (2, 3, 4). Find also the perpendicular distance of the origin from this plane.

Find a unit vector normal to the plane through the points (1, 1, 1), (-1, 2, 3) and (2, -1, 3) .

The equation of the plane passing through the mid point of the line points (1, 2, 3) and (3, 4, 5) and perpendicular to it is

Find the coordinates of the point where the line through (3, 4, 1) and (5, 1, 6) crosses XY-plane.

KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-PRACTICE WORK

Find the value of a so that the four points with position vectors -hat...
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A plane meets the co-ordinate axes at A, B and C such that the centroi...
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Show that the plane through (1, 1, 1), (1,-1, 1) and (-7, 3, -5) is pe...
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The foot of perpendicular from the origin to the plane is (4, -2, -5) ...
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Find the equation of the plane passing through the point (-1,2, 1) and...
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Find the equation of the plane containing the line of intersection of ...
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Find the equation of the plane through the line of intersection of vec...
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Find the equation of the plane passing through the intersection of the...
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Find the cartesian equation of the plane| through the intersection of ...
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Find the equation of the plane passing through the intersection of the...
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In the following cases, determine whether the given planes are paralle...
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If the planes vecr.(hati+2hatj-3hatk)=7 and vecr.(lambdahati+2hatj-7ha...
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Find the distance of the point (2, 1, 0) from the plane 2x + y + 2z + ...
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If the points (1, 1, lambda) and (-3, 0, 1) be equidistant from the pl...
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Find the distance between the parallel planes x + y - z + 4 = 0 and x ...
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Find the distance between the parallel planes vecr.(2hati-3hatj+6hatk...
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If the distance of the plane x - y + z + lambda = 0 from the point (1,...
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The direction cosines of two lines are 1, -2,-2 and 0, 2, 1. Find the ...
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The direction cosines of two lines are given by the following equation...
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Show that the line passing through the points (4, 7, 8) and (2, 3, 4) ...
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