linear algebra compute vectors

||u||=2
||v||=3
||w||=5
u dot v = -1
u dot w = 1
v dot w = -4

Compute:
a. ||-4w||
b. (u+w) dot v
c. ||u+v||^2
d. ||v-4w||^2

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asked by Kay
  1. a. k||X|| = ||kX|| assuming k is a scalar.

    b. Distributivity of multiplication over addition,
    (A+B).C = A.C + B.C

    c. Let R=U+V (vectorial addition)
    then vectors U, V and R form a triangle.
    The magnitude of R can be found by the cosine rule:
    R²=||U||²+||V||²-||U|| ||V||cos(θ)
    But ||U||cos(θ)=U.V/||V||
    So
    R²=||U||²+||V||²-||V||*(U.V/||V||)
    ||U||²+||V||²-U.V

    d. See (c), substituting -4W for V.

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