SOLUTION: What is the angle Θ between the two vectors u=<3,4> and v<2,1>

Algebra ->  Vectors -> SOLUTION: What is the angle Θ between the two vectors u=<3,4> and v<2,1>      Log On


   

Question 1197954: What is the angle Θ between the two vectors u=<3,4> and v<2,1>
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

What is the angle theta between the two vectors u=<3,4> and v<2,1>
The angle theta between two vectors u+and v is related to the modulus (or magnitude) and scaler (or dot) product of u+and v by the relationship:

u%2Av=+abs%28u%29%2Aabs%28v%29%2Acos%28theta%29
first find dot product:

u%2Av=<3,4>*<2,1>
u%2Av=3%2A2+%2B4%2A1
u%2Av=10

now find the modulus:

abs%28u%29=sqrt%283%5E2%2B4%5E2%29=sqrt%2825%29=5
abs%28v%29=sqrt%282%5E2%2B1%5E2%29=sqrt%285%29
their product:
abs%28u%29%2Aabs%28v%29=5sqrt%285%29

plug all in formula above:
10=+5sqrt%285%29%2Acos%28theta%29
10%2F%285sqrt%285%29%29=cos%28theta%29
2%2Fsqrt%285%29=cos%28theta%29
theta=cos%5E-1%282%2Fsqrt%285%29%29
theta=0.463647609-> radians
theta=26.57°