6.1 Vectors

A standard notation for a vector in the plane is a coordinate pair, such as 2, 5 . This represents the vector that has its tail at the origin and its head at the point with x coordinate 2 and y coordinate 5. Another standard notation for this vector is . Here and denote the unit vectors in the x and y directions, respectively.

In Mathematica, a vector in the plane is expressed as a list of length two, such as {2, 5}. Vector addition and scalar multiplication work exactly as you would expect:

  In[1]:= <b class="bold">{2, 5} + {17, <span class="unicode">?</span>4}</b>Out[1]= {19, 1}  In[2]:= <b class="bold"><span class="unicode">?</span>4{2, 5}</b>Out[2]= {<span class="unicode">?</span>8, <span class="unicode">?</span>20}  In[3]:= <b class="bold">i = {1, 0};</b><b class="bold">              j = {0, 1};</b><b class="bold">              2i + 5j</b>Out[5]= {2, 5}

Higher-dimensional vectors are simply given as longer lists. Here is the sum of two vectors in three-space:

<span class="inlinemediaobject"><a NAME="IMG_669"> href="portalcontent.asp?bkid=31099&image_src=https://images.books24x7.com/bookimages/id_31099/fig263%5F02%5F0%2Ejpg&image_id=669&previd=IMG_669"> target="_parent"><img alt="Image from book"> border="0"> height="87"> id="IMG_669"> src="https://images.books24x7.com/bookimages/id_31099/fig263_02.jpg"> title="Click To expand"> width="224"></a></span>