Define the points P(2,-2) and Q(3,-4). Carry out the following calculation.

Find two vectors parallel to vector QP with length 2.

The parallel vector of length 2 with the same direction is (?,?)

(exact answers, radicals where needed)

Two vectors parallel with vector QP are:

and .

The parallel vector with same direction is:

Step-by-step explanation:

The vector between points P and Q belongs to the following vector family:

The norm of this vector is determined by using the definition of norm:

The unit vector associated to the abovementioned vector family is:

The parallel vector of length 2 with same direction is obtained by multyplying the previous data by 2:

Two vectors parallel with vector QP are:

and .

The parallel vector with same direction is:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

this answer is !