*30. mmh Vector  has a magnitude of 12.3 units and points due west. Vector  points due north. (a) What is the magnitude of  if  has a magnitude of 15.0 units? (b) What is the direction of   relative to due west? (c) What is the magnitude of   if   has a magnitude of 15.0 units? (d) What is the direction of  relative to due west?

 

So for parts (a) and (b) we have the vectors looking as they did in Problem 1.23

The vectors  and  are at right angles so we can use Pythagorean theorem.

 

 

Squaring both sides and rearranging we can solve for B

 

 

Take square root of both sides

 

Plugging in values

 

 

 

To get angle since we are given  and   these are adjacent and hypotenuse, so use

 

 

 

 

for parts (c) and (d) again, we have the vectors looking as they did in Problem 1.23

Again, the vectors  and  are at right angles so we can use Pythagorean theorem.  Moreover the values are all the same as part (a) so the answer is again

 

 

For the angle again everything is the same except  points more south than north but values are same so we find

 

 

Please send any comments or questions about this page to ddonovan@nmu.edu

This page last updated on January 11, 2020