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Write vector \vec{AB} that goes from point A (1,1, 4) to point B (3,0, 1) .

Question:

Write vector {eq}\vec{AB} {/eq} that goes from point {eq}A (1,1,-4) {/eq} to point {eq}B (3,0,-1) {/eq}.

Vector:

If a quantity possesses both magnitudes as well as direction then the quantity is known as a vector quantity. Geometrically, a vector quantity is represented by an overhead arrow that indicates the direction.

Answer and Explanation:


Given

{eq}A (1,1,-4) {/eq} and {eq}B (3,0,-1) {/eq}


We have to find {eq}\vec{AB} {/eq}

$$\begin{align} \overrightarrow{AB} &=\text{Position vector of B}-\text{Position vector of A}\\ &=(x_2-x_1, y_2-y_1, z_2-z_1)\\ &=(3-1, 0-1, -1-(-4))\\ &=\left ( 2,-1, 3 \right )\\ &=2\hat{i}-\hat{j}+3\hat{k} \end{align} $$


Learn more about this topic:

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Vectors: Definition, Types & Examples

from Common Entrance Test (CET): Study Guide & Syllabus

Chapter 57 / Lesson 3
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