Three Dimensional Geometry
The Cartesian equations of a line are 2x−1=3y+2=−1z−5. Its vector equation is
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The distance between the line r⃗ .2i^−2j^+3k^+λ(i^−j^+4k^) and the plane r⃗ .(i^−5j^+k^)=5 is
If r=(i^+2j^+3k^)+λ(i^−j^+k^) and r=(i^+2j^+3k^)+μ(i^+j^−k^) are two lines, then the equation of acute angle bisector of two lines is
If the lines −3x−1=2ky−2=−2z−3and3kx−1=1y−5=−5z−6 are at right angle, then find the value of k˙
ABC is a triangle and A=(2,3,5),B=(-1,3,2) and C= (λ,5,μ). If the median through A is equally inclined to the axes, then find the value of λ and μ
Let L be the line of intersection of the planes 2x+3y+z=1 andx+3y+2z=2. If L makes an angle α with the positive x-axis, then cos αequals
Find the vector equation of the line passing through (1,2,3)
and parallel to the planes ri^−j^+2k^˙andr3i^+j^+k^˙=6.
A line makes angles α,β,γandδ
with the diagonals of a cube. Show that cos2α+cos2β+cos2γ+cos2δ=4/3.
What is the distance between the planesx−2y+z−1=0 and−3x+6y−3z+2=0?