Three Dimensional Geometry
Find a unit vector normal to the plane x−2y+2z=6.
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Find the equation of the line passing through the points (1,2,3)and(−1,0,4)˙
The line which passes through the origin and intersect the two lines x−12=y+34=z−53,x−42=y+33=z−144, is
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?
Two system of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a', b', c' respectively from the origin, then1a2+1b2+1c2=k(1a′2+1b′2+1c′2), where k is equal to
is parallel to vector α=−3i^+2j^+4k^
and passes through a point A(7,6,2)
and line L2
is parallel vector β=2i^+j^+3k^
and point B(5,3,4)˙
Now a line L3
parallel to a vector r=2i^−2j^−k^
intersects the lines L1andL2
at points CandD,
respectively, then find ∣∣CD∣∣˙
Which one of the following is the plane containing the lien x−22=y−33=z−45 and parallel to z axis?
A variable plane passes through a fixed point (a,b,c)
and cuts the coordinate axes at points A,B,andC˙
Show that eh locus of the centre of the sphere OABCisxa+yb+zc=2.
Find the values p
so that line 31−x=2p7y−14=2z−3and3p7−7x=1y−5=56−z
are at right angles.