Chapter 3, Problem 1MCQ

To determine

The option which is associated with the x component of a vector in Cartesian axes.

Answer to Problem 1MCQ

Option (a).

Explanation of Solution

The angle is a measured to be positive in the anticlockwise direction. For a vector in the Cartesian coordinate system, when the measurement is from the positive x axis then the $x$ and $y$ components is given by cosine and sine functions of the angle respectively

Conclusion:

Since the measurement in the positive axis give the cosine value of angle for the $x$ component of a vector, option (a) is correct.

The y component of a vector in Cartesian coordinate is associated with the sine value, option (b) is incorrect.

It is not possible to give the tangent of a value as the $x$ component of a vector in Cartesian system, option (c) is incorrect.

Since the measurement in the positive axis give the cosine value of angle for the $x$ component of a vector, option (d) is incorrect.