<p>K I do not understand question 41 in College Board’s Official Math 1 and 2 Study Guide book, fourth (last) test page 170. It goes:</p>
<li>If n distinct planes intersect in a line, and another line l intersects one of these planes in a single point, what is the least number of these n plaes that l could intersect?</li>
</ol>
<p>a. n
b. n-1
c. n-2
d. n/2
e. (n-1)/2</p>
<p>im pretty sure the answer is n-1. This is because you have to intersect all of the planes except for one, which can be parallel to the plane you draw.</p>
<p>yea that is the answer, but can some explain why? I do not understand what CB means by ‘n distinct planes intersect in a line’…if i knew what this means i mite understand the rest.</p>
<p>bump. 10char.</p>
<p>bump…CAN NOBODY EXPLAIN THIS QUESTION FOR ME!? PLEASE NEED HELP!</p>
<p>Actually I was a little confused by this question as well, and while I sort of understand the answer, I certainly don’t know how to explain it well.</p>
<p>I’m not really sure either. But I think distinct means that they don’t touch each other.</p>
<p>Well, I’ll try my best to explain it; sorry if I don’t make any sense.</p>
<p>If n planes all intersect all in a line and another line l intersects one of the planes then you might think that the line intersects all of the planes. However, exactly one of the planes could be parallel to line l - so line l must intersect all but one of the planes. So the answer is n-1.</p>
<p>Ya its n-1. The only plane it might not intersect is the plane thats parallel to the line…its kinda hard to visulize…try smaller cases for n.</p>
<p>Ok yea I am sort of getting a better understanding of it now…I understand that if line l is parallel to a plane then it will not intersect it, but what does the question mean by “If n distinct planes intersect in a line”…?</p>
<p>When two lines intersect, they intersect at a point, however, when two planes intersect, they intersect at a line. Just try to visualize the intersection of two infinite planes in 3D space.</p>
<p>Wow I don’t get it at all. </p>
<p>Oh well, I’ll just fail math… my supposed good subject.</p>
<p>If you take some sheets of paper and make a physical diagram it might be easier to “visualize”.</p>
<p>So if there are 4 planes that intersect in a line, then it would be impossible for another line to intersect more or less than 3 of these planes? </p>
<p>I mean, I get it kind of, but I would never have been able to get it on test day (in a decent amount of time). It would be one of the ones I’d skip. I hate the roman numeral questions too…</p>
<p>Yes because lines and planes are infinite.^</p>
<p>^ No! It could intersect all four planes, but the question was asking for the least planes it could intersect. The least number of planes is n-1 because one, and only one plane may be parallel to the line.</p>
<p>oh my bad i didnt read wehat he was saying…yea it could intersect all 4…the min is n-1.</p>
<p>the min is n-1 because the lines and planes go infiently out so it will have to intersect atleaset n-1 of them…but not n of them because parallels never intersect.</p>
<p>If it’s still hard for you to visualize it perhaps you should break it down into the smallest possible case. You must have at least two planes, which intersect and one line which intersects at least one of the planes. So the least number of planes the line could intersect would be 1 (n-1), since the two planes **could **be perpendicular.</p>