Question P2.4: In each case, establish F as a Cartesian vector, and find th......
In each case, establish F as a Cartesian vector, and find the magnitude of F and the direction cosine of β.
Step-by-Step
\begin{array}{lrl} \text { a. } & \mathbf{F}&=\{-4 \mathbf{i}-4 \mathbf{j}+2 \mathbf{k}\} \mathbf{k N} \\ & F&=\sqrt{(4)^2+(-4)^2+(2)^2}=6 \mathrm{kN} \\ &\cos \beta & =\frac{-2}{3} \\ \text { b. }& \mathbf{F} & =\{20 \mathbf{i}+20 \mathbf{j}-10 \mathbf{k}\} \mathrm{N} \\ &F & =\sqrt{(20)^2+(20)^2+(-10)^2}=30 \mathrm{~N} \\ &\cos \beta & =\frac{2}{3} \end{array}
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