Question

A vector points from the origin into the second quadrant of the xy plane. What can you conclude about its components? (a) Both components are positive. (b) The x component is positive, and the y-component is negative. (c) The x-component is negative, and the y-component is positive. (d) Both components are negative. (e) More than one answer is possible.

Short answer

The correct option is (c).

Step-by-step solution

Definition of quadrants

A two-dimensional Cartesian system's axes split the plane into four infinite areas called quadrants, each of which is delimited by two half-axes. The coordinates are commonly numbered from 1 to 4 and represented by Roman numerals: I (+, +), || (-, +), III (-, -), and IV (+, -).

Explanation for the correct option

Consider the diagram below, which depicts the coordinate system's partition into four quadrants.

Here, x and y are positive for a point in the | quadrant, || the quadrant x is negative, and both x and y are negative for the third quadrant. x is positive and y is negative if the point is in the fourth quadrant.

The issue specifies that the vector extends from the origin to the second quadrant.

Thex-component will be negative, whereas the y-component will be positive, as seen in the diagram.

Hence, option (c) is the correct choice.

Explanation for option (a)

The x-component will be negative and the y-component will be positive.

So, option (a) is incorrect.

Explanation for option (b)

The x-component will be negative and the y-component will be positive.

So, option (b) is incorrect.

Explanation for option (d) 

The x-component will be negative and the y-component will be positive.

Quadrant IV denotes (+, -).

So, option (d) is incorrect.

Explanation for option (e)

The x-component will be negative and the y-component will be positive.

So, option (e) is incorrect.