Math 115 (Assignments)

[To Be Turned in on Wednesday]

1. Use vectors and dot products to show that if the diagonals of a parallelogram are perpendicular, then the length of the sides are equal.

   Do not convert to coordiantes to do this. You should work entirely in terms of vectors, so should not mention coordinate anywhere. (The perallelogram could be in any dimension.) Instead, you should rely on the properties of the dot product, e.g., $\u\cdot\u=|\u|^2$. Remember that your conclusion should be that the lengths of the two sides are equal, so that is where you should end up, not where you start.

Be sure to indicate which properties of the dot product you are using at each step, and do not combine several steps into one. That is, use only one property at a time.




2. Consider the vector $\displaystyle\v(t)=\left<3-t,{t^2+18\over t+2}\right>$. Is $\v(t)$ ever parallel to the vector $\left<1,3\right>$? If so, for what value(s) of $t$, and what is the $\v(t)$?

Math 115 (Fall 2013) web pages Created: 14 Oct 2013 Last modified: Oct 16, 2013 10:55:11 AM Comments to: dpvc@union.edu

Assignments