$8/28/24,2$:$42$ PM

Addition of $3$D Cartesian Vectors

As shown, a pole is subjected to three forces: $F,P,$ and $T.$ The force $F$ expressed in Cartesian vector form is $F=[8i+8j+8k]N.$ Force $P$ has magnitude $7\mathrm{.}35$ N and acts in the direction given by these direction angles: $=114,=35\mathrm{.}3,$ and $=65\mathrm{.}9$ to the $x,y,$ and $z$ axes, respectively. Force $T-$lies within the $yz$ plane, its direction is given by the $34-5$ triangle shown, and its magnitude is $16$ N $.$

Part A $-$ Calculating the magnitude of a vector from its components

What is the magnitude of $F?$

Express your answer to three significant figures and include the appropriate units.

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ANSWER: