Three Dimensional Geometry
Find the vector and Cartesian equations of a plane which is at a distance of 5 units from the origin and which has 3i^−2j^+6k^ as the unit vector normal to it.
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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.
Value ofλ such that the linex−12=y−13=z−1λIs perpendicular to normal to the planer⃗ .(2i⃗ +3j⃗ +4k⃗ )=0 is
What is the angle between the planes2x−y+z=6 andx+y+2z=3?
If P(x,y,z) is a point on the line segment joining Q(2,2,4)andR(3,5,6) such that the projections of OP on the axes are 13/5, 19/5 and 26/5, respectively, then find the ratio in which P divides QR˙
If the x-coordinate of a point P
on the join of Q(22,1)andR(5,1,−2)is4,
then find its z−
A line makes the same angle α with each of the x and y axes. If the angleθ, which it makes with the z-axis, is such thatsin2θ=2sin2α, then what is the value ofα?
Find the angle between the lines whose direction cosines are connected by the relations l+m+n=0and2lm+2nl−mn=0.
Find the angle between the lines x−3y−4=0,4y−z+5=0andx+3y−11=0,2y=z+6=0.