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Question

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


A

¯a+λ¯b

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B

¯a+λ(¯a+¯b)

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C

¯b+λ(¯a¯b)

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D

¯aλ(¯a¯b)

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Solution

The correct options are
B

¯a+λ(¯a+¯b)


C

¯b+λ(¯a¯b)


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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