Answer:
Step-by-step explanation:
Let a,b be vectors. Then we know that a and b are orthogonal if [tex]a\cdot b =0[/tex], where [tex]\cdot[/tex] is the dot product. We also say that if
[tex]a= kb[/tex] for some positive scalar k, when a and b are in the same direction. If k is negative, then a and b are in opposite directions.
Note that c = -1*v. So c and v are in opposite directions. Also, note that w=3*u. so w and u are in the same direction. Note that since b=(0,1) and the others vectors have non-zero entries, this implies that none of the vectors are in the same direction nor opposite direction of b, given that 0 times any number is 0.
Note that [tex]a\cdot u = 1*(-2)+2*1 =0[/tex] so a and u are orthogonal. Since w is in the direction of u, this implies that a is orthogonal to w. We also have that v = 2a. So v is in the same direction of a. Hence, v is orthogonal to u and w.
Finally, note that [tex]b\cdot a = 2[/tex] , [tex]b\cdot u = 1[/tex]. So this implies that b is not orthogonal to any other vector in particular.
Answer:
(make sure you have a vector symbol above your vectors*)
orthog same opposite
a,u a,v a,v
a,w u,w u,w
c,u
c,w
u,v
v,w
Step-by-step explanation:
To find Orthogonal vectors, check if the dot product is equal to zero
ex: vectors a and u are orthogonal
[tex](1*-2)+(2*1)\\=-2+2\\=0[/tex]
To find same direction vectors, look for vectors that are scaled versions of other vectors
ex: vectors a and v are same direction
2(a)=v 2(1,2)=(2,4)
Opposite direction vectors are just the negative versions of other vectors (scaled by a negative number)
ex: vectors a and c are opposite
-2(a)=c -2(1,2)=(-2,-4)
*If you are coming from RSM:
To enter your answers, first, enter a ray symbol
(a depiction is attached)
