Question

question 5 (1 point) consider two vectors, $vec{a}$ and $vec{b}$ shown in the figure. the difference of vector $vec{a} - vec{b}$ is best illustrated by which of the following images? a) choice (a) b) choice (b) c) choice (c) d) choice (d)

Explanation:

Step1: Recall vector subtraction rule

Vector subtraction \(\vec{A} - \vec{B}\) is equivalent to \(\vec{A} + (-\vec{B})\), where \(-\vec{B}\) is the vector with the same magnitude as \(\vec{B}\) but opposite direction.

Step2: Analyze given vectors

\(\vec{A}\) is a vector pointing upwards (at an angle), \(\vec{B}\) is a vector pointing to the right. So \(-\vec{B}\) will point to the left.

Step3: Determine the resultant

To find \(\vec{A} - \vec{B}=\vec{A}+(-\vec{B})\), we add \(\vec{A}\) (up - angled) and \(-\vec{B}\) (left - pointing). The resultant vector should have a direction that combines the upward - angled direction of \(\vec{A}\) and the left - ward direction of \(-\vec{B}\). Looking at the options, option (c) has a vector that is angled in a way that combines the upward - left direction which is consistent with \(\vec{A}+(-\vec{B})\). Option (a) is vertical down, option (b) is down - right, option (d) is up - right. So the correct option should be (c).

Answer:

c) choice (c)