+0  
 
0
4411
3
avatar

determine whether u and v are orthogonal, parallel or neither.

 

u= (4,7) 

v= (-28,8)

 Jul 14, 2016

Best Answer 

 #2
avatar+33603 
+5

If the coordinates of u and v represent the heads of vectors that start at the origin, then the slope of u = 7/4 and the slope of v = -8/28 → -2/7

 

The slopes are not the same hence the lines are not parallel.

 

The slope of v is not -1/the slope of u, hence the lines are not orthogonal.

 Jul 15, 2016
 #1
avatar+14865 
0

Good evening Guest!

 

determine whether u and v are orthogonal, parallel or neither.

 

u= (4,7) 

v= (-28,8)

 

The slope of the function through the points u and v is

 

 \(m = \frac{y(u)-x(u)}{y(v)-x(v)} = \frac{7-4}{8+28} = \frac{1}{12} \) 

The connection line u - v is not perpendicular or parallel to the abscissa axis of the Cartesian coordinate system.
The slope to the abscissa is

\(m = \frac{1}{12} \)

I hope I have understood your question correctly.

 

Greeting asinus :- )

laugh   !

 Jul 14, 2016
 #2
avatar+33603 
+5
Best Answer

If the coordinates of u and v represent the heads of vectors that start at the origin, then the slope of u = 7/4 and the slope of v = -8/28 → -2/7

 

The slopes are not the same hence the lines are not parallel.

 

The slope of v is not -1/the slope of u, hence the lines are not orthogonal.

Alan Jul 15, 2016
 #3
avatar+128079 
+5

The vectors will be orthogonal if their dot product =  0  .....so we have

 

u (dot) v =  

 

4 * -28   +  7 * 8   =

 

-112 +  56   =   

 

-56  ...so they are not orthogonal

 

They will be parallel when either

 

u (dot) v   = ll u ll * ll v ll      or

 

u (dot) v  = - ll u ll * ll v ll

 

ll u ll  = √ [ 4^2 + 7^2]  = √ 65           and   ll v ll = √ [ 28^2 + 8^2]  = √ 848

 

So   - ll u ll *  ll v ll   =  - √ 65 * √ 848  = -√55120 = about  - 238.78    so.....this does not equal the dot product, so they are not parallel, either

 

 

cool cool cool

 Jul 15, 2016

4 Online Users

avatar
avatar