what are (a) the x components and (b) the y components of vector →a in the xy plane if it's direction is 249 degrees counterclockwise from the positive direction of the x axis and its magnitude is 9.4 m? 

To find the components of the vector \( \vec{a} \) in the \( xy \)-plane, we can break it down using trigonometry. Given:

- The direction of \( \vec{a} \) is \( 249^\circ \) counterclockwise from the positive \( x \)-axis.
- The magnitude of \( \vec{a} \) is \( 9.4 \, \text{m} \).

### Step 1: Understanding the angle
The vector's direction is measured counterclockwise from the positive \( x \)-axis, so the angle with respect to the positive \( x \)-axis is \( 249^\circ \).

To compute the components of \( \vec{a} \), we will use the following formulas:

\[
a_x = |\vec{a}| \cos(\theta)
\]
\[
a_y = |\vec{a}| \sin(\theta)
\]
where:
- \( |\vec{a}| = 9.4 \, \text{m} \) (the magnitude),
- \( \theta = 249^\circ \) (the angle with respect to the positive \( x \)-axis).

### Step 2: Calculating the \( x \)-component
\[
a_x = 9.4 \cos(249^\circ)
\]

### Step 3: Calculating the \( y \)-component
\[
a_y = 9.4 \sin(249^\circ)
\]

Now let's calculate these values.

The components of vector \( \vec{a} \) are:

(a) The \( x \)-component: \( a_x = -3.37 \, \text{m} \)

(b) The \( y \)-component: \( a_y = -8.78 \, \text{m} \)

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would the components change if the magnitude of the vector was doubled?
2. What are the \( x \)- and \( y \)-components if the angle was \( 90^\circ \) instead of \( 249^\circ \)?
3. Can you express the direction and magnitude of a vector given only its components?
4. What is the resultant vector if you add another vector with a direction of \( 120^\circ \) and a magnitude of \( 5 \, \text{m} \)?
5. How does the vector's angle affect the sign of its components?

**Tip:** Always ensure that the angle used is measured counterclockwise from the positive \( x \)-axis unless specified otherwise.

What are (a) the x components and (b) the y components of vector →a in the xy plane if its direction is 249 degrees counterclockwise from the positive direction of the x-axis and its magnitude is 9.4 m?

Learn how to calculate the x and y components of a vector with a magnitude of 9.4 m and a direction of 249 degrees from the positive x-axis. This problem involves vector components, trigonometry, and coordinate systems. Suitable for high school students (Grades 9-12).

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