SOLUTION: Find the angle between the vectors of U = 7i + 2j and V = -4j? Thanks.

Algebra ->  Test -> SOLUTION: Find the angle between the vectors of U = 7i + 2j and V = -4j? Thanks.      Log On


   

Question 1075779: Find the angle between the vectors of U = 7i + 2j and V = -4j? Thanks.
Answer by ikleyn(52818) About Me  (Show Source):
You can put this solution on YOUR website!
.
The dot product of these vectors is U*V = 7*0 + 2*(-4) = 0 - 8.


The length of the vector U is |U| = sqrt%287%5E2+%2B+2%5E2%29 = sqrt%2853%29.


The length of the vector V is |V| = sqrt%28%28-4%29%5E2%29 = sqrt%2816%29 = 4.


Then the cosine of the angle between the vectors U and V is 


cos%28alpha%29 = %28U%2AV%29%2F%28abs%28U%29%2Aabs%28V%29%29 = -8%2F%284%2Asqrt%2853%29%29 = -2%2Fsqrt%2853%29. 


Hence, alpha = arccos%28-2%2Fsqrt%2853%29%29.


Please complete calculations on your own from this point.

There are lessons on dot-product in this site that can be useful to you:
    - 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
    - Solved problems on Dot-product of vectors and the angle between two vectors

    - 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


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".