Question

Vector A is 12.4 cm long and is pointing in a direction which is 73.0 degrees from the positive axis, measured in a counter-clockwise direction. Vector B is 15.1 cm long and is pointing in a direction which is 156.0 degrees from the positive axis, measured in a counter-clockwise direction. Calculate the x and y components of these vectors.

Answer 1

Answer:

Explanation:

I will ASSUME you mean the positive X axis.

Ax = 12.4cos73.0  = 3.6254...

Ay = 12.4sin73.0   = 11.8581...

Bx = 15.1cos156.0 = -13.7945...

By = 15.1sin156.0  = 6.1417...

Answer 2

The x components of vector A is 3.62 cm and the  y components of vector A is 11.85 cm

The x components of vector B is -13.79 cm and the  y components of vector B is 6.14 cm

The given parameters;

length of vector A = 12.4 cm

length of vector B = 15.1 cm

angle of  vector A from the positive x-axis = 73⁰

angle of  vector B from the positive x-axis = 156⁰

To find:

• the  x and y components of these vectors

The x components of vector A:

$A_x = A \times cos (\theta)\\\\A_x = 12.4 \ cm \times \ cos (73)\\\\A_x = 3.62 \ cm$

The y components of vector A:

$A_y = A \times sin (\theta)\\\\A_y = 12.4 \ cm \times \ sin (73)\\\\A_y =11.85 \ cm$

The x components of vector B:

$B_x = B \times cos (\theta)\\\\B_x = 15.1 \ cm \times \ cos (156)\\\\B_x = -13.79 \ cm$

The y components of vector B:

$B_y = B \times sin (\theta)\\\\B_y = 15.1 \ cm \times \ sin (156)\\\\B_y = 6.14 \ cm$

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