Three Dimensional Geometry
Find the vector and Cartesian equations of the plane passing through the point (3,−1,2) and parallel to the lines r=(−j^+3k^)+λ(2i^−5j^−k^) and r=(i^−3j^+k^)+μ(−5i^+4j^).
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are the an gles which a directed line makes with the positive directions of the co-ordinates axes, then find the value of sin2α+sin2β+sin2γ˙
Find the distance of the point P(a,b,c)
from the x-axis.
Prove that the plane r=(i^+2j^−k^)=3
contains the line r=i^+j^+λ(2i^+j^+4k^)˙
Find the distance between the parallel planes x+2y−2z+1=0and2x+4y−4z+5=0.
Find ten equation of the plane passing through the point (0,7,−7)
and containing the line −3x+1=2y−3=1z+2
Determine whether the following pair of lines intersect or not. (1) r=i^−5j^+λ(2i^+k^);r=2i^−j^+μ(i^+j^−k^)
Find the image of the point (1,2,3) in the line 3x−6=2y−7=−2z−7.
If the lines −3x−1=2ky−2=−2z−3and3kx−1=1y−5=−5z−6 are at right angle, then find the value of k˙