SOLUTION: Suppose a = 2 i + 5 j and b = 9 i − 4 j a • b = I have this as -2 Also give the angle between the vectors in degrees to one decimal place. This is the par

Algebra ->  Vectors -> SOLUTION: Suppose a = 2 i + 5 j and b = 9 i − 4 j a • b = I have this as -2 Also give the angle between the vectors in degrees to one decimal place. This is the par      Log On


   

Question 1000518: Suppose
a = 2 i + 5 j and b = 9 i − 4 j
a • b =
I have this as -2
Also give the angle between the vectors in degrees to one decimal place.
This is the part I am stuck on
THANK YOU
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Scalar product of vectors a = 2i + 5j and b = 9i − 4j is

2*9 + 5*(-4) = 18 - 20 = -2.

Cosines of the angle between these two vectors is

cos%28alpha%29 = %28-2%29%2F%28sqrt%282%5E2+%2B+5%5E2%29%2Asqrt%289%5E2%2B4%5E2%29%29 = %28-2%29%2F%28sqrt%2829%29%2Asqrt%2897%29%29 = -0.03771.

alpha = arccos(-0.03771) = 1.6085 rad = 92°10'  (approximately).

About the angle between two vectors in a plane and how to calculate this angle using the scalar products of the vectors see the lesson
The formula for the angle between two vectors and the formula for cosines of the difference of two angles  in this site.