Q. 15
Find the Cartesian equation of a line which passes through the point having position vector 
and is in the direction of the vector 
Answer :
Given : A line which passes through the point having position vector 
and is in the direction of the vector 
To find : cartesian equations of a line
Formula used : If a line which passes through the point having position vector
p
+ q
+ r
and is in the direction of the vector l
+ m
+ n
then its Cartesian
equation is given by
= 
= 
A line which passes through the point having position vector 
and is in the direction of the vector 
Here l = 1 , m = 2 , n = -1 and p = 2 , q = -1 , r = 4
= 
= 
= 
= 
The Cartesian equation of a line which passes through the point having
position vector 
and is in the direction of the vector 
is
= 
= 
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Find the vector and Cartesian equations of the line through the point (1, 2, -4) and perpendicular to the two lines.
and 
Write the vector equations of the following lines and hence determine the distance between them:
