Question

Vector C is 6.28 units long in a 105° direction. In unit vector notation, this would be written as:

C = [? ] î + [?] j

Answer 1

Vector C with magnitude 6.28 units and direction of 105° can be written in unit vector notation as C = [-3.09] î + [5.40] j, using trigonometric functions to obtain its x and y components.

Step-by-step explanation:

The student's question involves finding the components of a vector given its magnitude and direction in degrees. To express the vector in unit vector notation, we can decompose it into its x and y components using trigonometric functions derived from its angle measurement. Since vector C has a magnitude of 6.28 units and a direction of 105°, we must calculate the x component (Cx) and the y component (Cy). The x component is found by multiplying the magnitude by the cosine of the angle, and the y component by multiplying the magnitude by the sine of the angle:

Cx = 6.28 × cos(105°)

Cy = 6.28 × sin(105°)

Using a calculator, we can find these values:

Cx ≈ -3.09 (since cos(105°) is negative)

Cy ≈ 5.40

Therefore, vector C in unit vector notation can be expressed as:

C = [-3.09] î + [5.40] j