Yes.
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yes
Yes, provided it is the ray. If AB is a vector then the answer is no.
[(aa + bb) + (ab+ba)(aa+bb)*(ab+ba)]*[a + (ab+ba)(aa+bb)*b]
no; commutative
naming a line is different from naming a ray. say for example ,if we have line AB,this is similar to line BA while ray AB is different from ray BA.