June 8th, 2017, 08:07 AM  #1 
Member Joined: May 2017 From: Slovenia Posts: 89 Thanks: 0  Vectors again
Find the area of parallelogram given by the vectors e=2mn and f=4m5n. m=n=1 and the angle between m and n is pi/4. I really struggle with this one and any help is appreciated 
June 9th, 2017, 03:44 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,159 Thanks: 866 
The area of a parallelogram is, of course, given by "bh" where b is the length of one side (the "base" which we can take to be e) and h the height. If $\displaystyle \theta$ is the angle between the two sides, then $\displaystyle h= \tan(\theta)e$ so that the area is $\displaystyle \tan(\theta)ef$. Here, you are given that e= f= 1 and $\displaystyle \theta$ is $\displaystyle \pi/4$ radians. Last edited by skipjack; June 9th, 2017 at 06:14 AM. 
June 9th, 2017, 05:50 AM  #3  
Member Joined: May 2017 From: Slovenia Posts: 89 Thanks: 0  Quote:
Last edited by skipjack; June 9th, 2017 at 06:15 AM.  
June 9th, 2017, 06:21 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,956 Thanks: 1602 
Yes. Country Boy slipped up. What's stopping you from evaluating e × f?

June 9th, 2017, 06:45 AM  #5 
Member Joined: May 2017 From: Slovenia Posts: 89 Thanks: 0  I did this, but the textbook says I'm wrong.

June 9th, 2017, 09:28 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 18,956 Thanks: 1602 
What does the textbook give as the answer?

June 9th, 2017, 09:32 AM  #7 
Member Joined: May 2017 From: Slovenia Posts: 89 Thanks: 0  Last edited by skipjack; June 9th, 2017 at 07:55 PM. 
June 9th, 2017, 10:06 AM  #8  
Math Team Joined: Jul 2011 From: Texas Posts: 2,751 Thanks: 1401  Quote:
if so ... $e = \left(2\dfrac{1}{\sqrt{2}}\right)i  \left(\dfrac{1}{\sqrt{2}}\right)j$ $f = \left(4\dfrac{5}{\sqrt{2}}\right)i  \left(\dfrac{5}{\sqrt{2}}\right)j$ however, this makes $e \times f = 3\sqrt{2}$ ?  
June 9th, 2017, 08:09 PM  #9 
Global Moderator Joined: Dec 2006 Posts: 18,956 Thanks: 1602 
The answer depends on the meaning of "given by the vectors" in the problem. If the specified vectors correspond to the sides of the parallelogram, the area is 3√2. If the vectors correspond to the diagonals of the parallelogram, the area is 3/√2.

June 10th, 2017, 12:12 AM  #10 
Member Joined: May 2017 From: Slovenia Posts: 89 Thanks: 0  It's the sides. Probably it's just mistake in the textbook Thank you.


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