Three Dimensional Geometry
If (2, 3, 5) is one end of a diameter of the sphere x2+y2+z2−6x−12y−2z+20=0, then the coordinates of the other end of the diameter are
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Find the vector equation of a line passing through 3i^−5j^+7k^
and perpendicular to theplane 3x−4y+5z=8.
Prove that the plane r=(i^+2j^−k^)=3
contains the line r=i^+j^+λ(2i^+j^+4k^)˙
What is the acute angle between the planes x+y+2z=3 and −2x+y−z=11?
Find the equation of the plane passing through (3,4,−1),
which is parallel to the plane r2i^−3j^+5k^˙+7=0.
Find the equation of the plane through the points (23,1)and(4,−5,3)
and parallel to the x-axis.
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
A line OP
through origin O
is inclined at 300and450→OXandOY,
respectivley. Then find the angle at which it is inclined to OZ˙
Value ofλ such that the linex−12=y−13=z−1λIs perpendicular to normal to the planer⃗ .(2i⃗ +3j⃗ +4k⃗ )=0 is