SOLUTION: Find the angle between u=〈-2​,−1〉 and v=〈−1​,2〉 to the nearest tenth of a degree.

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Question 1138912: Find the angle between u=〈-2​,−1〉 and v=〈−1​,2〉 to the nearest tenth of a degree.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
u=〈-2​,−1〉 , v=〈−1​,2〉
cos%28theta%29 =%28u%2Av%29/(||u||*||v||) where %28u%2Av%29 is scalar product, ||u|| and ||v|| are the lengths of vectors u and v
Calculate the length of each vector. Picture a right triangle drawn from the vector's x-component, its y-component, and the vector itself. The vector forms the hypotenuse of the triangle, so to find its length we use the Pythagorean theorem. As it turns out, this formula is easily extended to vectors with any number of components.
||u|| =+sqrt%28u%5B1%5D%5E2+%2B+u%5B2%5D%5E2%29+
||u|| = %28%28-2%29%5E2+%2B+%28-1%29%5E2%29
||u|| =+sqrt%284%2B+1%29+
||u|| =+sqrt%285%29+
||v|| =+sqrt%28v%5B1%5D%5E2+%2B+v%5B2%5D%5E2%29+
||u|| =+sqrt%28%28-1%29%5E2+%2B+2%5E2%29
||u|| =+sqrt%285%29
Calculate the dot product of the two vectors.
u%2Av=u%5B1%5Dv%5B1%5D+%2B+u%5B2%5Dv%5B2%5D
u%2Av=%28-2%29%28-1%29+%2B+%28-1%29%282%29
u%2Av=2-2
u%2Av=0
Plug your results into the formula.
cos%28theta%29 =%28u%2Av%29/(||u||*||v||)
cos%28theta%29+=0%2F%28sqrt%285%29+%2Asqrt%285%29+%29+
cos%28theta%29+=0
theta=cos%5E-1%280%29+
theta=pi%2F2
theta=90°