Ong Qian Wei's answer to Sonia's Junior College 2 H2 Maths Singapore question.

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Ong Qian Wei
Ong Qian Wei's answer
6 answers (A Helpful Person)
1st
Hope you’re able to see :)
1) a•b is a scalar, so basically vector a is just a scalar multiple of vector b. They have to be in the same direction, but provided a•b is positive. Otherwise they are opposite directions.
Vector b has to be a unit vector because Vector a is the vector projection along vector b, which based on the projection formula, Vector b has to be a unit vector.

2) geometrically sketch and show that OP is perpendicular to AP then try to move P around