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Points, Vectors, and Functions

Points, Vectors, and Functions

Points, Vectors, and Functions: Vexing Vectors Quiz

Think you’ve got your head wrapped around Points, Vectors, and Functions? Put your knowledge to the test. Good luck — the Stickman is counting on you!
Q. Which best completes the following sentence? "A vector is..."

a magnitude.
a quantity with both magnitude and direction.
a line segment with an arrow at one end.
an expression of the form .
Q. ||<3, -1>|| =

Q. Find the direction of the vector .

Q. Which of the following does NOT represent the vector whose x-component is 3 and whose y-component is 2?

<3, 2>
(3, 2)
3j + 2i
Q. Whether a function is a vector function or scalar function depends on

the input of the function.
the output of the function.
both the input and the output of the function.
the operations involved in computing the function.
Q. Which of the following are scalar functions? 

  1. f(x) = x2 
  2. g(x,y) = x + y 
  3. h(x,y) = ||<x, y>||

(I) only
(I) and (II)
(II) and (III)
(I), (II), and (III)
Q. Find f(4, 5) where the function f is defined by f(x, y) = <x + y, x y>

<9, -1>
<-1, 9>
Q. Determine which graph is the best representation of the function  for 0 ≤ t ≤ 4:

Q. A unit vector is

any scalar multiple of the vector <1, 1>.
any vector of the form <1, y> or <x, 1>.

a vector with integer components.
a vector with magnitude 1.
Q. To normalize the vector , it must be multiplied by

This vector is already normalized.