Vector A is in the direction 86.5 degree clockwise from -y axis. The x component of A is -91.3. What is the magnitude of A? The answer has no unit.

We are given that:

- Vector **A** is 86.5° clockwise from the negative y-axis.
- The x-component of **A** is \(-91.3\).

To find the magnitude of **A**, we first need to calculate the angle of the vector relative to the positive x-axis, then use the x-component to solve for the magnitude.

### Step 1: Find the angle relative to the x-axis

Since the vector is 86.5° **clockwise** from the negative y-axis, the angle relative to the positive x-axis (\(\theta\)) is:

\[
\theta = 270^\circ + 86.5^\circ = 356.5^\circ
\]

### Step 2: Use the x-component to find the magnitude

The x-component of a vector is given by:

\[
A_x = A \cos(\theta)
\]

Substituting the given x-component and the angle:

\[
-91.3 = A \cos(356.5^\circ)
\]

Since \(\cos(356.5^\circ)\) is approximately \(0.9962\), we can now solve for the magnitude of the vector **A**:

\[
-91.3 = A \times 0.9962
\]

\[
A = \frac{-91.3}{0.9962}
\]

Let's calculate this value.

\[
A \approx 91.65
\]

Thus, the magnitude of **A** is approximately **91.65**.

Would you like further details on any step or have more questions?

Here are 5 related questions:
1. How would the angle change if the vector was measured counterclockwise instead of clockwise?
2. What if the y-component of the vector was given instead of the x-component?
3. How can you find the direction of the vector if both components are known?
4. How do trigonometric functions like sine and cosine relate to vector components?
5. Can you determine the vector in component form using the magnitude and direction?

**Tip:** The magnitude of a vector is always positive, but its components (x and y) can be negative or positive depending on the direction.

Learn how to find the magnitude of a vector given its x-component (-91.3) and direction (86.5° clockwise from the -y axis). This trigonometry problem uses vector component formulas and cosine functions to calculate the vector's magnitude, suitable for students in Grades 9-12.

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