If v lies in the first quadrant and makes an angle 𝜋/3 with the positive x-axis and |v| = 10, find v in component form.

To find the vector v in component form, we can use the given information that v lies in the first quadrant and makes an angle 𝜋/3 with the positive x-axis.

Step 1: Draw a coordinate plane and label the x-axis and y-axis.

Step 2: Since v lies in the first quadrant, its x-component (v_x) will be positive and its y-component (v_y) will also be positive.

Step 3: The angle 𝜋/3 is equivalent to 60 degrees. Draw a line from the origin that makes a 60-degree angle with the positive x-axis.

Step 4: Since |v| = 10, the length of the vector v is 10 units. Draw a line segment from the origin to the point on the line that is 10 units away.

Step 5: The x-component of v (v_x) is the length of the line segment projected onto the x-axis. Measure this length and label it as v_x.

Step 6: The y-component of v (v_y) is the length of the line segment projected onto the y-axis. Measure this length and label it as v_y.

Step 7: Write the vector v in component form as v = (v_x, v_y).

By following these steps, you can find the vector v in component form.