Answer :
Answer:
[tex]\vec u = \frac{12\cdot \sqrt{30}}{5}\,\hat{i}-\frac{9\cdot \sqrt{30}}{5} \,\hat{k}[/tex]
Step-by-step explanation:
Vectors are represented by magnitude and direction, which is equivalent to the unit vector multiplied by a given magnitude:
[tex]\vec u = r\cdot \frac{\vec v}{\|\vec v\|}[/tex]
The magnitude of [tex]\vec v[/tex] is given by Pythagorean Theorem. If [tex]\vec v = 24\,\hat {i}-18\,\hat{k}[/tex], then:
[tex]\|\vec v\|=\sqrt{24^{2}+(-18)^{2}}[/tex]
[tex]\|\vec v\| = \sqrt{30}[/tex]
If [tex]r = 3[/tex], [tex]\vec v = 24\,\hat {i}-18\,\hat{k}[/tex] and [tex]\|\vec v\| = \sqrt{30}[/tex], then:
[tex]\vec u = \frac{72}{\sqrt{30}}\,\hat{i}-\frac{54}{\sqrt{30}} \,\hat{k}[/tex]
[tex]\vec u = \frac{12\cdot \sqrt{30}}{5}\,\hat{i}-\frac{9\cdot \sqrt{30}}{5} \,\hat{k}[/tex]