Question

the initial point of a vector v in v2 is the origin and the terminal point is in quadrant ii. if v makes an angle 5/6 with the positive x-axis and |v| = 10, find v in component form.

Answer 1

7.93 6.09 is the answer

Answer 2

(7.93, 6.09).

Explanation:

The vector v starts at the origin and ends in Quadrant II. We are given that v makes an angle of 5/6 with the positive x-axis and its magnitude (length) is 10.

To find v in component form, we can break down the vector into its x and y components. The x-component represents the horizontal displacement, while the y-component represents the vertical displacement.

Since the angle is measured from the positive x-axis, we can use trigonometric functions to find the x and y components of the vector.

The x-component can be found using cosine function:

x = |v| * cos(angle)

Substituting the given values:

x = 10 * cos(5/6)

To find the y-component, we use the sine function:

y = |v| * sin(angle)

Substituting the given values:

y = 10 * sin(5/6)

Now we have the x and y components of the vector v. The component form of v is (x, y).

To simplify further, we can use a calculator to find the values of x and y:

x ≈ 10 * 0.793 = 7.93

y ≈ 10 * 0.609 = 6.09

Therefore, v in component form is approximately (7.93, 6.09).