please help w/ "Find vector b given a = 3i - j, a*b = -6, angle between a, b is 30 degrees

[Lalala]

can someone help me solve this q please?

 

[Lalala]

this has to do w/ scalar/dot product. not sure where to go with this, was thinking simultaneous equations but im not getting the right answer

 

[BigBeachBanana]

[math]\bold{a \cdot b} = \bold{|a| \cdot |b|} \cdot \cos(\theta)[/math]
The LHS is given.
Find the magnitude of the vector [imath]\bold{|a|}[/imath]
Solve for the magnitude of the vector [imath]\bold{|b|}[/imath]
Find the components of [imath]\bold{b}[/imath]

 

[blamocur]

View attachment 36996
this has to do w/ scalar/dot product. not sure where to go with this, was thinking simultaneous equations but im not getting the right answer

There are two solutions, one for each direction of the angle (clockwise or counterclockwise).