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# Unit vector notation (part 2)

More on unit vector notation. Showing that adding the x and y components of two vectors is equivalent to adding the vectors visually using the head-to-tail method. Created by Sal Khan.

## Want to join the conversation?

• Why do vectors have to be arranged "head to tales" in order for the addition to work out?
• Think of it like walking,
I walked 3 meters left and 2 forward,
then I walked 2 meters right and 4 forward....
Where am I?
Wouldn't make sense to start both movements at the origin
• If we wanna add two vectors, we arrange them HEAD to TAIL right? then what if i wanna subtract them? how do you arrange vectors graphically when you subtract them?
• The vector you want to substract out must change to its opposite direction and then arrange graphically using the head-to-tail method.

If you have the vector (3, 2) and you want to substract it from other one, you change its direction to (-3, -2).
• SAL! You are someone to be believed, if not blindly then maybe after some thought. You are helping so many people's lives! (this happens at )
• In the graph, to get vectors a and b we rely on x and y axes which guarantee forming a right angle even if we need to do shifting. however, after getting vectors a and b (green and red arrows) at what guarantees that they will be perpendicular on each other and form a right angle?
for example: if vector b equation was b=2i+2j instead of b=2i+4j it will form an obtuse angle with vector a instead of right angle and trig functions will not work. what do we do in that case. and will the analytical way still valid with such equations?
• This is one of the biggest reasons that the unit vector notation exists. With it you don't have to have a right triangle or use obscure trigonometric functions.

Also, in the case of he video, the vectors aren't at right angles, even though they seem that way visually. If we multiply the directionless slope of the two vectors together and get anything but -1, then they are not perpendicular.

slope of vector a=2/-3 or -2/3
slope of vector b=4/2 or 2

since -2/3*2=/=-1 then the two vectors aren't perpendicular.
(1 vote)
• how would you subtract using the head-to-tail method?
• Please watch video for subtraction of vectors via the head-to-tail and the tail-to-tail methods. ~ http://youtu.be/mFu5IPOG5Cw
• can 2 vectors be added if one is in 2 dimension & the other one is in 3 Dimension ?
• Yes, here is an example.
A = a i + b j
B = d i + e j + f k
A + B = (a+d) i + (b+e) j + f k
• How would u visually subtract the vectors?
• keeping them on the same origin, you can connect their tips.
• how to find an angle between 2 vectors when both have equal magnitudes
• You'll need more information, tha magnitude of two vectors doesn't say the necessary things to discover the angle between they.