Question

Vector $\overrightarrow{\mathbf{A}}$lies in the$\mathit{x}\mathit{y}$ plane. Both of its components will be negative if it points from the origin into which quadrant?

(a) the first quadrant

(b) the second quadrant

(c) the third quadrant

(d) the fourth quadrant

(e) the second or fourth quadrants.

Short answer

The correct option is (c).

Step-by-step solution

Definition of quadrants

A two-dimensional Cartesian system's axis 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; ,$\text{I}\left(+,+\right)$ ,$\text{II}\left(-,+\right)$,$\text{III}\left(-,-\right)$ and $\text{IV}\left(+,-\right)$.

Explanation for correct option

The coordinate system is divided into four quadrants.

If both$x$and$y$components of a vector are negative and the vector starts from the origin, then the vector will point towards the third quadrant.

As a result option (c) is correct choice.

Explanation for option (a)

In first quadrant both x and y components of a vector are positive.

So, option (a) is incorrect.

Step 4: Explanation for option (b)

In second quadrant x component is negative and y component is positive.

So, option (b) is incorrect.

Explanation for option (d).

In fourth quadrant x component is positive and y component is negative.

So, option (b) is incorrect.

Explanation for option (e) 

From the option (b) and (d), it is clear that option (e) is also incorrect choice.