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### Course: Precalculus>Unit 6

Lesson 5: Vector addition and subtraction

# Parallelogram rule for vector addition

The parallelogram rule says that if we place two vectors so they have the same initial point, and then complete the vectors into a parallelogram, then the sum of the vectors is the directed diagonal that starts at the same point as the vectors. Created by Sal Khan.

## Want to join the conversation?

• I really like Sal's more recent approach to videos. This one is so simple yet so comprehensive.
Thanks Sal. Thanks to the team.
• For tips and thanks
(1 vote)
• Could you prove addition for integers is commutative using this principle(since adding integers is the same as adding a vector with y component zero to a point in the complex plane)?
• The content make sense for me but I have one question: Is it possible to add the head of vector a and b together, instead of adding a vector's tail to the other's head?
(1 vote)
• According to the derivation of this law (that i found in google) it was resultant vector = sqroot of (p^2+q^2+2pqcostheta). Here p,q is are two sides and p is the initial side and q is the terminal side. Sal said p+q=r.
but this is not what derivation says the value for r is entirely different [sqroot of (p^2+q^2+2pqcostheta)].Isnt this law incorrect
(1 vote)
• Don't confuse a vector with its magnitude. If p and q are vectors, and the sum of these two vectors is the vector r, then we simply write p+*q*=r.

If we say that p has magnitude p and q has magnitude q, then the magnitude of r is given by your formula (which is essentially just the law of cosines).
(1 vote)
• I didn't really understand it. If 2 small sides of a triangle are always more than the remaining side, then how if ->a + ->b = ->c. Shouldn't their sum be more than ->c
(1 vote)
• this method is dumb and confusing