Answer:
A) The vectors are parallel.
B) The vectors are not parallel.
Step-by-step explanation:
A) - Vector v1 has a component equal to [tex]\sqrt{3}[/tex] in x and a component equal to [tex]1[/tex] in y.
- Vector v2 has a component equal to [tex]\sqrt{3}[/tex] in the direction -x and a component equal to [tex]1[/tex] in in the direction -y.
- This means that both vector are parallel. You can prove this by applying the cross product and veriying that the result is zero.
[tex]\left[\begin{array}{ccc}i&j&k\\\sqrt{3}&1&0\\-\sqrt{3}&-1&0\end{array}\right]\\\\v_1\ x\ v_2 = k[\sqrt{3}(-1) - (1)(-\sqrt{3})]\\\\v_1\ x\ v_2 = 0[/tex]
B) Let's make the cross product between both. If they are parallel then the result will be zero.
[tex]\left[\begin{array}{ccc}i&j&k\\2&3&0\\-3&-2&0\end{array}\right]\\\\\\u_1\ x\ u_2 = k(-4 - (-9))\\u_1\ x\ u_2 = 5k\\u_1\ x\ u_2 \neq 0[/tex]
Then the vectors are not parellel
