Find Equation of a straight line which passes through the points given by position vectors ¯a and ¯b .
¯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 ¯a−λ (¯a−¯b) and ¯b+λ (¯a−¯b). Therefore answers are both options c and d.