Three Dimensional Geometry
Show that the distance of the point of intersection of the line 3x−2=4y+1=12z−12 and the plane x−y+z=5 from the point (−1,−5,−10) is 13 units.
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The equation of the line which passes through the point (1, 1, 1) and intersect the lines x−12=y−23=z−34 and x+21=y−32=z+14 is
If the straight lines x=−1+s,y=3−λs,z=1+λsandx=2t,y=1+t,z=2−t,
with paramerters sandt,
respectivley, are coplanar, then find λ˙
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
The equations of motion of a rocket are x=2t,y=−4tandz=4t,
is given in seconds, and the coordinates of a moving points in kilometers. What is the path of the rocket? At what distance will be the rocket from the starting point O(0,0,0)
Find the equation of the plane passing through A(2,2,−1),B(3,4,
Also find a unit vector perpendicular to this plane.
Find the equation of a line which passes through the point (2,3,4)
and which has equal intercepts on the axes.
The extremities of a diameter of a sphere lie on the positive y- and positive z-axes at distance 2 and 4, respectively. Show that the sphere passes through the origin and find the radius of the sphere.
Find the equation of the line passing through the points (1,2,3)and(−1,0,4)˙