The vector equation of a plane is vecr.(...

The vector equation of a plane is `vecr.(2hati+2hatj-hatk)=21`, find the length of the perpendicular from the origin to the plane.

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Vector equation of a plane is vecr.(2hati+4hatj-3hatk)=5 . Write down the equation of the plane in the cartesian form.

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

Find the cartesian equation of the following planes. vecr.(hati+hatj-hatk)=2

Find the vector equation of a line passing through the point with position vector (2hati-3hatj-5hatk) and perpendicular to the plane vecr*(6hati-3hatj-5hatk)+2=0 . Also, find the point of intersection of this line and the plane.

Find the equations of the plane through the intersection of the planes vecr.(hati-1hatj)=-6 and vecr.(3hati+3hatj-4hatk)=0 , whose perpendicular distance form the origin is unity.

Find the vector equation of the line passing through the point (1,2,1) and perpendicular to the plane vecr.(2hati-hatj+hatk)=10 . Find the point of intersection of this line and the plane.

A line passing through the point A with position vector veca=4hati+2hatj+2hatk is parllel to the vector vecb=2hati+3hatj+6hatk .Find the length of the perpendicular drawn on this line from a point P with position vector vecr_1=hati+2hatj+3hatk .

Find the cartesian equation of the following planes. vecr.(2hati+hatj-4hatk)=1 .

Find the cartesian equation of the following planes: vecr.(2hati-3hatj-4hatk)=1

Find the equation of the plane which contain the line of intersection of the plane vecr.(hati+2hatj+3hatk)-4=0 and vecr.(2hati+hatj-hatk)+5=0 and which is perpendicular to the plane 5x+3y-6z+8=0 .

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE

Find the vector equations of the line passing through the point (1,-1,...
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Find the vector equation of the line through the origin, which is perp...
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The vector equation of a plane is vecr.(2hati+2hatj-hatk)=21, find the...
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Find the vector equation of a plane which is at a distance of 5 units ...
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Find the vector equation of a line passing through the point with posi...
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The foot of perpendicular drawn from the origin to a plane is (12,-4,-...
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The foot of perpendicular drawn from the origin to a plane is (2,5,7)....
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O is the origin and A is (a,b,c). Find the d.c. of OA and the equation...
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Find the equation of the plane whose intercepts on the axes are 3,4,5 ...
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Find the equation of the plane passing through the point (2,4,6) and m...
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A variable plane moves so that the sum of reciprocals of its intercept...
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A plane meets the coordinates axes in A, B and C such that the centroi...
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Find the intercepts made by the plane 2x-3y+5z+4=0 on the co-ordinate ...
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Change to normal form the plane 2x-3y+6z+4=0
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Find the vector equation of the following planes in scalar product for...
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Find the shortest distance between the following lines whose vector eq...
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Find the vector equation of the following plane in scalar product form...
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Find the equation satisfied by the coordinates of a variable point P(x...
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Find the vector equations of the plane passing through the points R(2...
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Prove that the normal to the plane containing three point whose positi...
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