Answer:
A) The vectors are parallel.
B) The vectors are not parallel.
Explanation:
A) - Vector v1 has a component equal to
in x and a component equal to
in y.
- Vector v2 has a component equal to
in the direction -x and a component equal to
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.
![\left[\begin{array}{ccc}i&j&k\\√(3)&1&0\\-√(3)&-1&0\end{array}\right]\\\\v_1\ x\ v_2 = k[√(3)(-1) - (1)(-√(3))]\\\\v_1\ x\ v_2 = 0](https://img.qammunity.org/2020/formulas/mathematics/high-school/ivz98re0ftf2sa4kd91vnzt7k9eszzuvlu.png)
B) Let's make the cross product between both. If they are parallel then the result will be zero.
![\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 \\eq 0](https://img.qammunity.org/2020/formulas/mathematics/high-school/d38bihdbmkpsssv9nvpkprnu9ub5khb9uo.png)
Then the vectors are not parellel