What are (a) the x component and (b) the y component of a vector in the xy plane if its direction is 259° counterclockwise from the positive direction of the x axis and its magnitude is 5.4 m?

(a) -1.030m

(b) -5.301m

Given a vector F in the xy plane, of magnitude F and in a direction θ counterclockwise from the positive direction of the x-axis;

The x-component () of vector F is given by;

= F cos θ    ---------------------(i)

And;

The y-component () of vector F is given by;

= F sin θ            -----------------------(ii)

Now to the question;

Let the vector be A

Therefore;

The magnitude of vector A is A = 5.4m

The direction θ of A counterclockwise from the positive direction of the x-axis = 259°

(a) The x-component () of the vector A is therefore given by;

= A cos θ       ------------------------(iii)

Substitute the values of θ and A into equation (iii) as follows;

= 5.4 cos 259°

= 5.4 x (-0.1908)

= -1.030

Therefore, the x-component of the vector is -1.030m

(b) The y-component () of the vector A is therefore given by;

= A sin θ       ------------------------(iv)

Substitute the values of θ and A into equation (iv) as follows;

= 5.4 sin 259°

= 5.4 x (-0.9816)

= -5.301m

Therefore, the y-component of the vector is -5.301m