Q. 94.2( 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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