Three Dimensional Geometry
A line segment has length 63 and direction ratios are 3,−2,6. The components of the line vector are
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From the point P(1,2,4) a perpendicular is drawn on the plane 2x+y−2z+3=0. Find the equation, the length and the coordinates of the foot of the perpendicular.
A line passes through the point A(5,−2,4) and it is parallel to the vector (2i^−j^+3k^ ). The vector equation of the line is
Write the vector equation of each of the following lines and hence determine the distance between them:2x−1=3y−2=6z+4 and 4x−3=6y−3=12z+5.
Find the length and the foot of the perpendicular drawn from the point (1,1,2) to the plane r⋅(2i^−2j^+4k^)+5=0.
The Cartesian equations of a line are 3x+1=6y−2=1−z. Find the fixed point through which it passes, its direction ratios and also its vector equation.
A line is perpendicular to two lines having direction ratios 1,−2,−2 and 0,2,1. The direction cosines of the line are
Show that the points A(2,1,3),B(5,0,5) and C(−4,3,−1) are collinear.
If the equations of a line are −33−x=−2y+2=6z+2, find the direction cosines of a line parallel to the given line.