Class 12

Math

3D Geometry

Three Dimensional Geometry

If the cartesian equations of a line are $53−x =7y+4 =42z−6 $, write the vector equation for the line

Let, $53−x =7y+4 =42z−6 =t$

$53−x =t$

or, $x=3−5t$

Similarly,

$y=7t−4$ and $z=2t+3$

Now, $r=xi^+yj^ +zk^$

or, $r=(3−5t)i^+(7t−4)j^ +(2t+3)k^$

or, $r=(3i^−4j^ +3k^)+t(−5i^+7j^ +2k^)$