To express the vector $\vec{A}$ in terms of the unit vectors $\hat{i}$ and $\hat{j}$, we can use the following steps:

1. Determine the components of vector $\vec{A}$:

   • The magnitude of $\vec{A}$ is $3.60$ meters.
   • The angle $\theta_A$ that $\vec{A}$ makes with the positive x-axis is $70.0^\circ$.

2. Calculate the components of $\vec{A}$:

   • The x-component ($A_x$) is given by: $A_x = A \cos(\theta_A) = 3.60 \cos(70.0^\circ)$
   • The y-component ($A_y$) is given by: $A_y = A \sin(\theta_A) = 3.60 \sin(70.0^\circ)$

3. Express $\vec{A}$ in unit vector notation: $\vec{A} = A_x \hat{i} + A_y \hat{j}$

Now let's compute the components:

$A_x = 3.60 \cos(70.0^\circ) \approx 1.23 \, \text{meters}$ $A_y = 3.60 \sin(70.0^\circ) \approx 3.38 \, \text{meters}$

Thus, the vector $\vec{A}$ in unit vector notation is:

$\vec{A} \approx 1.23 \hat{i} + 3.38 \hat{j} \, \text{meters}$

Do you want details or have any questions?

Here are 5 related questions:

1. How do you find the unit vector of a given vector?
2. What is the significance of the angle between the vector and the x-axis?
3. How would the components change if vector $\vec{A}$ was in the second quadrant?
4. How can you determine the direction of a vector using its components?
5. What role does trigonometry play in vector decomposition?

Tip: Always ensure your calculator is set to the correct mode (degrees or radians) when calculating trigonometric functions.