Three Dimensional Geometry
Find the vector and Cartesian equations of a plane which is at a distance of 296 from the origin and whose normal vector from the origin is (2i^−3j^+4k^).
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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 line whose direction cosines are given by l+m+n=0and2l2+2m2−n2−0.
A point P(x,y,z) is such that 3PA=2PB, where AandB are the point (1,3,4)and(1,−2,−1), irrespectivley. Find the equation to the locus of the point P and verify that the locus is a sphere.
The centre of the circle given by ri^+2j^+2k^˙=15and∣∣r−(j^+2k^)∣∣=4 is
a. (0,1,2) b. (1,3,5) c. (−1,3,4) d. none of these
Find the locus of a point, the sum of squares of whose distance from the planes x−z=0,x−2y+z=0 and x+y+z=0 is 36
Find the distance between the line −3x+1=2y−3=1z−2
and the plane x+y+z+3=0.
Find the equation of the plane passing through the line 5x−1=6y+2=4z−3 and point (4,3,7)˙
Find the equation of line x+y−z−3=0=2x+3y+z+4
in symmetric form. Find the direction of the line.