Calculus II/Vector Geometry Operation

Addition and Subtraction

File:VectorOperations.png

If $𝐚$ and $𝐛$ are vectors,

Then the sum

$𝐜=𝐚+𝐛$ is also a vector (see Figure 2(a)).

The two vectors can also be subtracted from one another to give another vector

$𝐝=𝐚-𝐛$.

Multiplication by a scalar

Multiplication of a vector $𝐛$ by a scalar $\lambda$ has the effect of stretching or shrinking the vector (see Figure 2(b)).

You can form a unit vector $\widehat{𝐛}$ that is parallel to $𝐛$ by dividing by the length of the vector $|𝐛|$. Thus,

$\widehat{𝐛}=\frac{𝐛}{|𝐛|}.$