<PRE><B>Question 1199829</B>
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Unit vectors i,j,k are defined as such
i = &lt;1,0,0&gt;
j = &lt;0,1,0&gt;
k = &lt;0,0,1&gt;
When combined, they form the 3D xyz axis.


i+j = &lt;1,0,0&gt; + &lt;0,1,0&gt;
i+j = &lt;1+0,0+1,0+0&gt;
i+j = &lt;1,1,0&gt;


Then apply the dot product
k dot (i+j) = &lt;0,0,1&gt; dot &lt;1,1,0&gt;
k dot (i+j) = 0*1 + 0*1 + 1*0
k dot (i+j) = 0


The zero dot product result tells us that vector k is perpendicular (aka orthogonal) to vector i+j
In fact, any linear combination m*i+n*j, such that m and n are scalars, will be orthogonal to vector k.


Answer: &lt;font color=red size=4&gt;0&lt;/font&gt;
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