u=(:2,-4 :) and v=(: 5,-3:). Find the angle between them to the nearest tenth of a degree.

Edward Hendricks 2022-08-12 Answered
u = 2 , 4  and  v = 5 , 3 . Find the angle between them to the nearest tenth of a degree
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Answers (1)

Melany Flynn
Answered 2022-08-13 Author has 12 answers
Given vectors u=2i-4j, v=5i-3j
Angle between the two given vectrors,
cos θ = u v | u | | v | ( 1 ) u v = ( 2 ) ( 5 ) + ( 4 ) ( 3 ) = 10 + 12 = 22 | u | = ( 2 ) 2 + ( 4 ) 2 | u | = 4 + 16 | u | = 20 = 2 5 | v | = 5 2 + ( 3 ) 2 | v | = 25 + 9 | v | = 34
Substituting in the equation (1),
cos θ = u v | u | | v | cos θ = 22 ( 2 5 ) ( 34 ) cos θ = 11 ( 4.472 ) ( 5.830 ) cos θ = 11 26.071 cos θ = 0.4219 θ = cos 1 ( 0.4219 ) θ = 65
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