SOLUTION: Has this problem been resolved correctly? Find the angle between two vectors u=3i+4j and v=5i-4j 3 + 4 and 5 − 4 3 * 5 + 4 * −4 15 + −16

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Question 1202786: Has this problem been resolved correctly?
Find the angle between two vectors u=3i+4j and v=5i-4j
3 + 4 and 5 − 4
3 * 5 + 4 * −4
15 + −16
-1
||u|| = √(3^2+4²) = √(9+16) = √25 = √5
||v|| = √(5^2+(-4)²) = √(25+16) = √41
θ = cos^1(-1/√205) = cos^1 (-(1/√205*√205/√205))
= cos⁡-√205/√205 = cos⁡√205/√205
Thank you
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

You have the correct dot product of -1.

The computation for ||u|| is incorrect. It should be 5 instead of sqrt%285%29

The computation for ||v|| is correct.

cos(theta) = ( u dot v )/( ||u||*||v|| )
cos(theta) = ( -1 )/( 5*sqrt(41) )
cos(theta) = -0.03123475237772
theta = arccos(-0.03123475237772)
theta = 91.789910608246 degrees

The result is approximate. Round it however needed.
The answer can be confirmed with GeoGebra.