Q. 9 4.2( 29 Votes )

. Find the vector and the cartesian equations of the line that passes through the points (3, –2, –5), (3, –2, 6).

Answer :

We know that

The vector equation of as line which passes through two points whose position vectors are and is .


Here, the position vectors of the two points (3, –2, –5) and (3, –2, 6) are and , respectively.


So, the vector equation of the required line is:





Now, we also know that


Cartesian equation of a line that passes through two points (x1, y1, z1) and (x2, y2, z2) is


So, the Cartesian equation of the line that passes through the origin (3, -2, -5) and (3, -2, 6) is



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