Three Dimensional Geometry
A line passes through the points (6,−7,−1)and(2,−3,1)˙
Find te direction cosines off the line if the line makes an acute angle with the positive direction of the x-axis.
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Find the acute angle between the lines lx−1=my+1=n1and=mx+1=ny−3=lz−1wherel>m>n,andl,m,n
are the roots of the cubic equation x3+x2−4x=4.
Find the vector equation of a line passing through 3i^−5j^+7k^
and perpendicular to theplane 3x−4y+5z=8.
Find the angle between the line r=(i+2j−k)+λ(i−j+k) and the normal to the plane r(2i−j+k)˙=4.
What are the direction cosines of a line which is equally inclined to the positive directions of the axes?
Find the equation of the line passing through the points (1,2,3)and(−1,0,4)˙
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
The shortest distance from the plane To the sphere is
The angle between the pair of planes represented by equation2x2−2y2+4z2+6xz+2yz+3xy=0is