Instructions Read the introduction  A vector in 2 dimensions (X and Y) can be decomposed into its X component and Y component. Each component is the magnitude, or length,
of the vector in that dimension. So, in the picture, the vector A has an X component of 2 and a Y component of 3.

Instructions Read the information and answer the question Goals Answer all questions
Submit your answers
 When we add vectors together, we add them componentwise. That is, we add the X components to get the X component of the resultant
vector and then we add the Y components to get the Y component of the resultant vector. As an example, if we have vector A = [2,3]and
vector B = [2,1] then when we add them the resultant vector C will be [4,2]. That's because the X component of A is 2 and the X
component of B is 2, so 2 + 2 = 4. Likewise, for the Y component of C: 3 + (1) = 2. Geometrically, this is the same as putting the
vectors headtotail. So, to find A + B, just move B so that its tail (the end without the arrow) is stuck to the head of A. Then
you can draw a new vector from the tail of A to the head of B. That new vector is the resultant vector, C.
Given the image above, answer the questions below.
What is the X component of vector C?
What is the Y component of vector C?

Instructions Read the information and answer the question Goals Answer all questions
Submit your answers
 Vector subtraction is componentwise just like addition, but when we want to see vector subtraction geometrically it helps to think
about it differently. In general we know that "A  B" is the same as "A + (B)". Well, that holds for vectors as well. With vectors
"B" is the same magnitude, or length, as "B" but it points in the opposite direction. For example if B is the vector [1,3] then B
is the vector [1,3]. Then you can just use the same headtotail system you used to add vectors.
If you want to treat the vectors involved in the subtraction as "position vectors" then there's yet another way you can think about
it! A position vector is a vector that describes a position in space. That is, if we translate (slide) the vector so that its tail is at
the origin then its head points to a position which is the same as the X and Y components of the vector. In that situation "A  B" is
like asking the question "What direction and how far do I need to travel from B to get to A?" If A and B are both position vectors
then their tails are at the origin. Geometrically then, "A  B" is the vector you draw from the head of B to the head of A. Something
to notice is that the resultant vector here is the same vector as it was in the headtotail method, it's just translated.
Really, you can use either method but you might have to translate the result in order to answer the question you're actually asking.
Given the image above, answer the questions below.
What is the X component of vector C?
What is the Y component of vector C?

Instructions Drag vectors from the surrounding area and connect them to guide the robot to the minerals. Goals Get the robot to the minerals
 You are in control of a small robot sent to survey a rift system and collect minerals on the newly discovered planet Kepler42. The robot is equipped with a short range
teleportation module that allows several smaller vectors to be input which will be added together in a series of jumps to reach a destination.
Your mission is to find the series of vectors for teleportation that will allow the robot to traverse the rift safely.
Drag vectors from the surrounding area and connect them end to end to guide the robot to its destination. (They'll snap to the yellow points).
Some vectors will need to be negated (made negative) for the path to make sense. Just click on a vector and then click "Negate Last Clicked Vector" to negate that
vector. All the vectors will be used and there are multiple configurations that will solve the problem.

Instructions You have completed the lesson. You may scroll up to review the lesson. 