Three Dimensional Geometry
For the following planes, find the direction cosines of the normal to the plane and the distance of the plane from the origin.z=3.
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The plane x+3y+13=0 passes through the line of intersection of the planes 2x−8y+4z=pand3x−5y+4z+10=0. If the plane is perpendicular to the plane3x−y−2z−4=0, then the value of p is equal to
If θ is the acute angle between the diagonals of a cube, then which one of the following is correct?
The angle between the straight lines r⃗ =(2−3t)i⃗ +(1+2t)j⃗ +(2+6t)k⃗ and r⃗ =(1+4s)i⃗ +(2−s)j⃗ +(8s−1)k⃗ is
Find the shortest distance between the lines 2x−1=3y−2=4z−3and3x−2=4y−4=5z−5
Prove that the plane r=(i^+2j^−k^)=3
contains the line r=i^+j^+λ(2i^+j^+4k^)˙
Find Cartesian and vector equation of the line which passes through the point (−2,4,−5)
and parallel to the line given by 3x+3=5y−4=6z+8
Find the equation of the plane containing the lines 4x−5=4y−7=−5z+3and7x−8=1y−4=3z−5˙
Find the angle between the line r=(i+2j−k)+λ(i−j+k) and the normal to the plane r(2i−j+k)˙=4.