Three Dimensional Geometry
The Cartesian equations of a line are 2x−1=3y+2=15−z. Find its vetor equation.
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The plane ax+by=0
is rotated through an angle α
about its line of intersection with the plane z=0.
Show that he equation to the plane in the new position is aby±za2+b2andα=0.
Find the image of the point (1,2,3) in the line 3x−6=2y−7=−2z−7.
What is the equation of the plane through z-axis and parallel to the linex−1cosθ=y+2sinθ=z−30?
Find the equations of the bisectors of the angles between the planes 2x−y+2z+3=0and3x−2y+6z+8=0
and specify the plane which bisects the acute angle and the plane which bisects the obtuse angle.
Find the equation of a plane containing the line of intersection of the planes x+y+z−6=0and2x+3y+4z+5=0
passing through (1,1,1)
Find the equation of the
line passing through the intersection of 2x−1=3y−2=4z−3and5x−4=2y−1=z˙
and also through the point (2,1,−2)˙
The vector equation of the line of intersection of the planes r⃗ =b⃗ +λ1(b⃗ −a⃗ )+μ1(a⃗ −c⃗ ) and r⃗ =b⃗ +λ2(b⃗ −c⃗ )+μ2(a⃗ +c⃗ )a⃗ ,b⃗ ,c⃗ being non-coplanar vectors, is
Find the distance between the parallel planes x+2y−2z+1=0and2x+4y−4z+5=0.