Q19 of 112 Page 1121

Find the vector and Cartesian equations of the line joining the points whose position vectors are and

Given: line passes through the points whose position vectors are and


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 (1 - 1) : (-2 - 3) : (1 + 2)


⇒ 0 : -5 : 3


⇒ 0 : 5 : -3


So,


Therefore,


Vector form:



Cartesian form:



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