Question

Select the answer that correctly shows the following vectors, given in component form, in standard position: v=(2,3).

a) (-2, -3)
b) (2, 3)
c) (-3, 2)
d) (3, 2)

Answer 1

The vector v=(2,3) when shown in standard position starts at the origin and has its head at (2,3), which means option b) (2, 3) is the correct way to represent this vector.

Step-by-step explanation:

To show a vector in component form in standard position, we start at the origin of a coordinate system and plot the vector according to its components along the x and y-axes. In this case, the vector given is v=(2,3). The correct representation of this vector in standard position is simply the vector itself with its tail at the origin (0,0) and its head at the coordinates (2,3). Thus, when drawn on a coordinate plane, its x-component stretches 2 units to the right along the x-axis, and its y-component stretches 3 units upwards along the y-axis. Therefore, the correct answer showing the vector v=(2,3) in the standard position is option b) (2, 3). The other options represent different vectors with either different magnitudes or directions.