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Question

Find Equation of a straight line which passes through the points given by position vectors ¯a and ¯b .


A

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B

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C

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D

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Solution

The correct options are
B


C


Let’s see the figure of the line,

If you look closely, the line which passes through points given by position vectors ¯a and ¯b is parallel to ¯a¯b which makes it a problem of finding the equation of a line given a point and parallel to a line. Therefore, equation of the line will be ¯a+λ (¯a¯b) or ¯b+λ (¯a¯b),λϵIR . Again without loss of generality. ¯a+λ (¯a¯b) can be modified to ¯aλ (¯a¯b) and ¯b+λ (¯a¯b). Therefore answers are both options c and d.


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