Consider the vectors vec$(a)=($:$1,4,-7$:$),$vec$(b)=($:$3,-4,5$:$),$ and vec$(c)=(-6,5,4$:$).$

a$.$ What are the direction angles $,,$ and $$ of the vector vec$(a)?$

$=$

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b$.$ What is the angle between the vectors vec$(a)$ and vec$(b)?$

c$.$ What is the area of the parallelogram formed by the vectors vec$(a)$ and vec$(b)?$

d$.$ What is the volume of the parallelepiped formed by the vectors vec$(a),$vec$(b),$ and vec$(c)?$

e$.$ Interpreting vec$(a),$vec$(b),$ and vec$(c)$ as position vectors, write a scalar equation of the plane passing through their terminal points.