Find the component form of v given its magnitude and the angle it makes with the positive x-axis. Sketch v.

Magnitude Angle
||v||= 7/2 45 degrees

v=( , )

x = |v| cos 45°

y = |v| sin 45°

surely you can sketch the vector.

To find the component form of vector v, we need to break it down into its x-component and y-component.

Given the magnitude of v, ||v|| = 7/2, and the angle it makes with the positive x-axis, which is 45 degrees, we can use trigonometry to find the x-component and y-component of v.

First, let's find the x-component (v_x):
Using cosine, we can calculate v_x = ||v|| * cos(angle):
v_x = (7/2) * cos(45 degrees) ≈ (7/2) * 0.707 ≈ 4.949

Next, let's find the y-component (v_y):
Using sine, we can calculate v_y = ||v|| * sin(angle):
v_y = (7/2) * sin(45 degrees) ≈ (7/2) * 0.707 ≈ 4.949

Therefore, the component form of vector v is: v = (4.949, 4.949).

To sketch the vector v, start at the origin (0,0), move 4.949 units to the right along the x-axis, and then move 4.949 units upwards along the y-axis. Mark the endpoint of the vector as (4.949, 4.949).