Problem $3.$ Recall that the Vector data type represents a vector and supports the following API:

$2$ vector.Vector

Vector$($a$)$ constructs a new vector v with Cartesian coordinates taken from the list a

v$[$i$]$ returns the ith coordinate of v

v $+$ w returnsthesumofv andw

v $-$ w returns the difference of v and w

v$.$scale$($alpha$)$ returns the scalar product of float alpha and v

v$.$dot$($w$)$ returns the dot product of v and w

v$.$direction$()$ returns the unit vector in the same direction as v

abs$($v$)$ returns the magnitude of v

len$($v$)$ returns the dimensions of v

str$($v$)$ returns a string representation of v

Now suppose you have a $5-$dimensional vector v $=(1,3,2,6,4).$

a$.$ What is the syntax for creating a Vector object v that represents the vector v$?$

A $$v $=$ Vector$(-1,3,2,6,4)$

B $$v $=[-1,3,2,6,4]$

C $$v $=$ Vector.$\_\_$init$\_\_([-1,3,2,6,4])$

D $$v $=$ Vector$([-1,3,2,6,4])$

E $$v $=$ Vector.$\_\_$init$\_\_(-1,3,2,6,4)$

b$.$ What is the syntax for computing the dot product of the vectors v and $2$v$?$

A $$v$.$dot$($Vector$.$scale$($v$,2))$

B $$v$.$dot$(2*$ v$)$

C $$Vector$.$dot$($Vector$.$scale$($v$,2))$

D $$Vector$.$dot$($v$,2*$ v$)$

E $$v$.$dot$($v$.$scale$(2))$

c$.$ What is the dot product of the vectors v and $2$v$?$ d$.$ What does the code abs$($v$)$ translate to internally?

A $$v$.\_\_$abs$\_\_($self$)$

B $$v$.\_\_$abs$\_\_()$

C $\_\_$abs$\_\_($self$,$ v$)$

D $$v$.$abs$()$

E $$self$.\_\_$abs$\_\_($v$)$

e$.$ What does abs$($v$)$ return?

f$.$ Suppose x and y are two Vector objects. What does the code x $+$ y translate to internally?

A $$Vector$.\_\_$add$\_\_($y$,$ x$)$

B $$Vector$.\_\_$add$\_\_($x$,$ y$)$

C $$x$.\_\_$add$\_\_($y$)$

D $\_\_$add$\_\_($x$,$ y$)$

E $$y$.\_\_$add$\_\_($x$)$

g$.$ What does len$($v$)$ return?

h$.$ What does the code str$($v$)$ translate to internally?

A $$v$.\_\_$str$\_\_($self$)$

B $$v$.$str$()$

C $$self$.\_\_$str$\_\_($v$)$

D $$v$.\_\_$str$\_\_()$

E $$str$($self$,$ v$)$