What is the angle $\phi$ between $\vec{a}=3.0 \hat{\mathrm{i}}-4.0 \hat{\mathrm{j}}$ and $\vec{b}=$ $-2.0 \hat{\mathrm{i}}+3.0 \hat{\mathrm{k}}$ ? (Caution: Although many of the following steps can be bypassed with a vector-capable calculator, you will learn more about scalar products if, at least here, you use these steps.)
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