Question

PLEASE HELP! ANSWER BOTH PARTS!

Answer 1

A) The vectors are parallel.

B) The vectors are not parallel.

Explanation:

A) - Vector v1 has a component equal to
`√(3)` in x and a component equal to
`1` in y.

- Vector v2 has a component equal to
`√(3)` in the direction -x and a component equal to
`1` 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`

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`

Then the vectors are not parellel