Question

vector a is due west and vector b is due north. which of the following represents the subtraction of vector a - vector b?

Explanation:

Step1: Recall Vector Subtraction Rule

Vector subtraction \( \vec{A} - \vec{B} \) is equivalent to \( \vec{A} + (-\vec{B}) \). The negative of a vector \( \vec{B} \) (which is due North) will be a vector of the same magnitude but opposite direction, i.e., due South.

Step2: Analyze Components of \( \vec{A} \) and \( -\vec{B} \)

• \( \vec{A} \) is due West, so its direction is along the negative x - axis (assuming standard coordinate system where East is positive x - axis and North is positive y - axis).
• \( -\vec{B} \) is due South, so its direction is along the negative y - axis.

Step3: Determine the Resultant Direction

When we add \( \vec{A} \) (West) and \( -\vec{B} \) (South), the resultant vector \( \vec{A}-\vec{B} \) should be in the direction of West - South (third quadrant in the standard coordinate system, where both x and y components are negative).

Looking at the options:

• The first option has a vector in the North - West direction (positive y and negative x), which is incorrect as \( -\vec{B} \) is South (negative y).
• The second option has a vector in the South - West direction (negative y and negative x), which matches our analysis of \( \vec{A}+(-\vec{B}) \) (since \( \vec{A} \) is West (negative x) and \( -\vec{B} \) is South (negative y)).
• The third option has a vector in the South - East direction (negative y and positive x), which is incorrect as \( \vec{A} \) is West (negative x).
• The fourth option has a vector in the North - East direction (positive y and positive x), which is incorrect.

Answer:

The second option (the one with the vector in the South - West direction labeled \( A - B \))