Three Dimensional Geometry
From the point P(1,2,4) a perpendicular is drawn on the plane 2x+y−2z+3=0. Find the equation, the length and the coordinates of the foot of the perpendicular.
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Find the shortest distance between the lines r=(1−λ)i^+(λ−2)j^+(3−2λ)k^andr=(μ+1)i^+(2μ+1)k^˙
Find the value of m for which thestraight line 3x−2y+z+3=0=4x+3y+4z+1 is parallel to the plane 2x−y+mz−2=0.
Find the angle between the line 3x−1=2y−1=4z−1
and the plane 2x+y−3z+4=0.
The equations of motion of a rocket are x=2t,y=−4tandz=4t,
is given in seconds, and the coordinates of a moving points in kilometers. What is the path of the rocket? At what distance will be the rocket from the starting point O(0,0,0)
The distance between the line r⃗ .2i^−2j^+3k^+λ(i^−j^+4k^) and the plane r⃗ .(i^−5j^+k^)=5 is
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
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.
Find the radius of the circular section in which the sphere ∣r∣=5
is cut by the plane ri^+j^+k^˙=33.