Consider the vectors u = 5 i + 4 j + 3 k , v = − 4 i − j − k and w = 4 i + 4 j − 5 k . Compute | 5 u − 4 v + w |

Question

Consider the vectors   u  =  5  i  +  4  j  +  3  k ,   v  =  −  4  i  −  j  −  k and   w  =  4  i  +  4  j  −  5  k . Compute       |    5  u  −  4  v  +  w      |

Donovan Shields · Accepted Answer

You are making an error when you say  ‖  5  u  −  4  v  +  w  ‖  =  5  ‖  u  ‖  −  4  ‖  v  ‖  +  ‖  w  ‖Note In general,   ‖  x  +  y  ‖  ≠  ‖  x  ‖  +  ‖  y  ‖There are couple of ways you can proceed:Either you can first compute the vector 5u−4v+w using basic vector algebra and then compute it&#039;s magnitude. ORYou can use the following                    ‖        a        +        b        +        c                  ‖          2                                    =        (        a        +        b        +        c        )        ⋅        (        a        +        b        +        c        )                                          =        a        ⋅        a        +        b        ⋅        b        +        c        ⋅        c        +        2        (        a        ⋅        b        +        b        ⋅        c        +        c        ⋅        a        )                                          =        ‖        a                  ‖          2                +        ‖        b                  ‖          2                +        ‖        c                  ‖          2                +        2        (        a        ⋅        b        +        b        ⋅        c        +        c        ⋅        a        )            Hopefully you can take it from here.

Consider the vectors u=5i+4j+3k , v=−4i−j−k and w=4i+4j−5k . Compute |5u−4v+w|

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