# Vector and scalar problem

This one:
a)Let V be a vector space and let x be a vector in V.
i)Show that b0=0 for each scalar b.
ii)Show that if bx=0, then either b=0 or x=0

## Answers and Replies

Im assuming you mean the magnitude.
The zero vector has components <0,0,0>, the magnitude of this vector is $$\sqrt{0^2+0^2+0^2} = 0.$$

b<x,y,z> = <bx,by,bz>

b<0,0,0> = <b0,b0,b0> = 0

ii) follows from i)

HallsofIvy