Q. 20

Find the vector equation of a line passing through the point A(3, -2, 1) and parallel to the line joining the points B(-2, 4, 2) and C(2, 3, 3). Also, find the Cartesian equations of the line.

Answer :

Given: line passes through the point (3, -2, 1) and is parallel to the line joining points B(-2, 4, 2) and C(2, 3, 3).


To find: equation of line in vector and Cartesian forms


Formula Used: Equation of a line is


Vector form:


Cartesian form:


where is a point on the line and with b1 : b2 : b3 being the direction ratios of the line.


Explanation:


Here,


The direction ratios of the line are (-2 - 2) : (4 - 3) : (2 - 3)


-4 : 1 : -1


4 : -1 : 1


So,


Therefore,


Vector form:



Cartesian form:



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