SOLUTION: Find the angle between the given vectors to the nearest tenth of a degree. u = <-5, 8>, v = <-4, 8>

Algebra ->  Vectors -> SOLUTION: Find the angle between the given vectors to the nearest tenth of a degree. u = <-5, 8>, v = <-4, 8>      Log On


   

Question 1091437: Find the angle between the given vectors to the nearest tenth of a degree.
u = <-5, 8>, v = <-4, 8>
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Use the two expressions of the vector dot product:
u • v = +abs%28u%29%2Aabs%28v%29+%2A+cos%28theta%29+=+u%5Bx%5D%2Av%5Bx%5D+%2B+u%5By%5D%2Av%5By%5D+

=
= ++84+%2F+%28%289.43398%29%288.94427%29%29+
= ++84+%2F+84.38008+
= ++0.9955+
+theta+=+cos%5E-1%280.9955%29+=+highlight%28+5.4%5Eo+%29+
—
Check: which you will recall is the dot product found by multiplying corresponding vector components +u%5Bx%5Dv%5Bx%5D+%2B+u%5By%5Dv%5By%5D+

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
On dot-product, see the lessons in this site
    - Introduction to dot-product
    - Formula for Dot-product of vectors in a plane via the vectors components
    - Dot-product of vectors in a coordinate plane and the angle between two vectors
    - Perpendicular vectors in a coordinate plane
    - Solved problems on Dot-product of vectors and the angle between two vectors
    - Properties of Dot-product of vectors in a coordinate plane
    - The formula for the angle between two vectors and the formula for cosines of the difference of two angles

    - HOW TO find dot-product of two vectors in a plane
    - HOW TO find scalar product of two vectors in a coordinate plane
    - HOW TO find the angle between two vectors in a coordinate plane
    - HOW TO prove that two vectors in a coordinate plane are perpendicular
    - HOW TO prove that a triangle in a coordinate plane is a right triangle
    - HOW TO check if a quadrilateral in a coordinate plane is a parallelogram
    - HOW TO check if a quadrilateral in a coordinate plane is a rectangle
    - HOW TO check if a quadrilateral in a coordinate plane is a rhombus
    - HOW TO check if a quadrilateral in a coordinate plane is a square


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Dot-product for vectors in a coordinate plane".