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If the angle between the vectors $\hat{i}-m \hat{j}$ and $\hat{j}+\hat{k}$ is $\frac{\pi}{3}$, then what is the value of $m ?$
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$\cos \frac{\pi}{3}=\frac{(\hat{\mathrm{i}}-\mathrm{m} \hat{\mathrm{j}}) \cdot(\hat{\mathrm{j}}+\hat{\mathrm{k}})}{\left|\sqrt{1+\mathrm{m}^{2}}\right|\left|\sqrt{1^{2}+1^{2}}\right|}$
$\frac{1}{2}=\frac{-\mathrm{m}}{\sqrt{1+\mathrm{m}^{2}} \cdot \sqrt{2}}$
$\frac{1}{2}=\frac{-\mathrm{m}}{\sqrt{1+\mathrm{m}^{2}} \cdot \sqrt{2}}$
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