Question

question 10
\\(\vec{v}=(9,4)\\)
solve: the unit vector of \\(\vec{v}\\)s y component is ____? (answer to 3 decimal places)

Explanation:

Step1: Calculate vector magnitude

The magnitude of vector $\vec{v}=(9,4)$ is $|\vec{v}|=\sqrt{9^{2}+4^{2}}=\sqrt{81 + 16}=\sqrt{97}\approx9.849$.

Step2: Calculate x - component of unit vector

The x - component of the unit vector of $\vec{v}$ is $\frac{v_x}{|\vec{v}|}$, where $v_x = 9$. So it is $\frac{9}{\sqrt{97}}\approx\frac{9}{9.849}\approx0.914$.

Step3: Calculate y - component of unit vector

The y - component of the unit vector of $\vec{v}$ is $\frac{v_y}{|\vec{v}|}$, where $v_y = 4$. So it is $\frac{4}{\sqrt{97}}\approx\frac{4}{9.849}\approx0.406$.

Answer:

The unit vector of $\vec{v}$'s X component is $0.914$.
The unit vector of $\vec{v}$'s Y component is $0.406$.