u = ⟨ 2 , − 4 ⟩ and v = ⟨ 5 , − 3 ⟩. Find the angle between them to the nearest tenth of a degree

Question

u  =  ⟨  2  ,  −  4  ⟩   and   v  =  ⟨  5  ,  −  3  ⟩. Find the angle between them to the nearest tenth of a degree

Melany Flynn · Accepted Answer

Given vectors u=2i-4j, v=5i-3jAngle between the two vectors that are given,  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          ∘

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

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