Tiny abstract vectors problem

Hi Mr Koh,

                   I encountered this question. It says: if  a = (a•b) b, where a and b are vectors, what are the possible angles between a and b?  Also, what is the magnitude of vector b?

Student X

a = (a•b) b  actually implies a is parallel to b.  Note that a•b is in fact a scalar quantity, such that a=kb, where we can set a•b = k . In view of this, the only possible angles between a and b would be 0 and 180 degrees.

To discover |b|, we shall proceed to take modulus of both sides of the original equation a = (a•b) b ; this gives us |a| = |a•b| |b| = [ |a| |b| ] |b| = |a| |b|^2 . Cancelling |a| on both sides leads to |b|^2 =1, and thus |b|=1 (shown)

Hope this helps. Peace.

Best Regards,

Mr Koh