May 27th, 2017, 09:56 PM  #1 
Newbie Joined: May 2017 From: Tanzania Posts: 8 Thanks: 0  Vector parallel to the line
Hi Guys! I was doing a vector math problem and I got stuck on how to find the vector parallel to the line. The question is : Determine if the plane given by x+2z=10 and the line given by r=(5,2t,10+4t) are orthogonal, parallel or neither. Now I have already found the normal vector as the first step, but also I have to find the vector that is parallel to the line so as that I can cross it with the normal vector to prove if it they are parallel to each other. Thank you. Last edited by skipjack; May 27th, 2017 at 11:56 PM. 
May 28th, 2017, 12:00 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,137 Thanks: 1415 
Is there a point that lies in the given plane and on the given line?

May 28th, 2017, 12:12 PM  #3  
Math Team Joined: Jan 2015 From: Alabama Posts: 2,819 Thanks: 750  Quote:
In general, a vector in the direction of the line $\displaystyle x= x_0+ At$, $\displaystyle y= y_0+ Bt$, $\displaystyle z= z_0+ Ct$ is <A, B, C>. Last edited by skipjack; May 29th, 2017 at 11:10 PM.  
May 29th, 2017, 05:55 AM  #4  
Newbie Joined: May 2017 From: Tanzania Posts: 8 Thanks: 0  Quote:
#Slumerican Last edited by skipjack; May 29th, 2017 at 11:10 PM.  
May 29th, 2017, 11:25 AM  #5 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,174 Thanks: 90 
A tad faster might be: A normal to plane is (1,0,2) by inspection. Line is r=(5,2,10)+t(0,1,4) (1,0,2)x(0,1,4)=0 [Note by moderator: (1, 0, 2) × (0, 1, 4) = (2, 4, 1)] Last edited by skipjack; May 29th, 2017 at 10:59 PM. 

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line, parallel, vector 
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