Question

A vector lying in the xy plane has components of opposite sign. The vector must lie in which quadrant?
A. 1st quadrant
B. 2nd quadrant
C. 3rd quadrant
D. 4th quadrant
E. Either 2nd or 4th quadrant

Answer 1

Hint:A vector in a plane is represented by a directed line segment (an arrow). The endpoints of the segment are called the initial point and the terminal point of the vector. An arrow from the initial point to the terminal point indicates the direction of the vector. The length of the line segment represents its magnitude.

Complete answer:
On a Cartesian plane, a quadrant is one of the four parts. Each quadrant contains a mix of positive and negative $x$ and $y$ values. The Cartesian plane is divided into four graph quadrants. Each graph quadrant contains a unique mix of positive and negative numbers.

The graph quadrants and their values are as follows:
-The first quadrant is located in the plane's upper right-hand corner. In this quadrant, both $x$ and $y$ have positive values.
-The plane's second quadrant is located in the top left corner. In this quadrant, $x$ has negative values while $y$ has positive values.
-The third quadrant is located in the bottom left corner. In this quadrant, both $x$ and $y$ have negative values.
-Quadrant IV is located in the bottom right corner of the screen. In this quadrant, $x$ has positive values while $y$ has negative values.
If $x$ and $y$ are both positive, a vector with components (x,y) or (x,y) would be in the second or fourth quadrant, respectively.

Hence, the correct answer is option E.

Note:The region contained by the intersection of the X-axis and the Y-axis is known as a quadrant. When the two axes, the X-axis and the Y-axis, cross at $90^{\circ}$ on the cartesian plane, four zones are formed around it, which are known as quadrants. As a result, each plane contains four quadrants, each of which is defined by half of the axes. Quadrant I, Quadrant II, Quadrant III, and Quadrant IV are the names given to each quadrant depending on their position relative to the axes.