<ol>
<li>If the magnitudes of vectors a and b are 5 and 12, then the magnitude of vector (b-a) could NOT be</li>
</ol>
<p>Ans: 5. </p>
<ol>
<li>If n distinct planes intersect in a line, and another line l intersects one of these planes in a single pint, what is the least number of these n planes that l could intersect?</li>
</ol>
<p>Ans: n-1</p>
<ol>
<li>In how many ways can 10 people be divided into two groups, one with 7 people and the other with 3?</li>
</ol>
<p>Ans: 120.</p>
<p>1: The smallest possible resultant of two vectors occurs when they are directly opposed (it will equal the difference of the two vectors). In this problem the smallest possible resultant is 7 (12-5)
2: Since the planes and the line extend infinitely, the only way the line will not intersect a given plane is if it is parallel to it. Since the planes are distinct, the line can only be parallel to one and therefore must intersect all the others. So the fewest planes the can intersect in n-1
3: Simple combination (use your calculator 10c7= 120)</p>