One displacement vector A has a magnitude of 2.43 km and points due north. A second displacemen

step 1 Alright, so here we're given two different vectors, vector A and vector B. We're told vector A h

One displacement vector A has a magnitude of 2.43 km and...

One displacement vector $\overrightarrow{\mathrm{A}}$ has a magnitude of $2.43 \mathrm{~km}$ and points due north. A second displacement vector $\overrightarrow{\mathbf{B}}$ has a magnitude of $7.74 \mathrm{~km}$ and also points due north. (a) Find the magnitude and direction of $\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}} \cdot(\mathrm{b})$ Find the magnitude and direction of $\overrightarrow{\mathrm{B}}-\overrightarrow{\mathrm{A}}$

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Key Concepts

Vector Magnitude

The magnitude of a vector is a measure of its length or size, and is typically calculated using the Pythagorean theorem for its components. In problems involving displacement or forces, finding the magnitude is essential to understand the scale of the vector quantity regardless of its direction.

Direction of Vectors

The direction of a vector specifies the way in which the vector is pointing, usually expressed in terms of angles relative to a reference direction such as north. This concept is important because vectors have both magnitude and direction, and understanding the direction helps in comprehensively describing their orientation and influence.

Vector Subtraction

This concept involves subtracting one vector from another by subtracting their corresponding components. In physics and engineering, the subtraction of vectors is used to determine relative displacement, velocity, and other quantities. The process takes into account both magnitude and direction, and can result in a vector pointing in a completely different direction than the original vectors.

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