Magnitudes of Vectors Don't Add Up
Date: 11/14/2010 at 02:15:12 From: David Subject: Why does the vector law of addition work? I don't understand how adding vectors results in
Magnitudes of Vectors Don't Add Up
Date: 11/14/2010 at 02:15:12 From: David Subject: Why does the vector law of addition work? I don't understand how adding vectors results in a triangle in which the third side is equivalent to the sum of the original two vectors. In particular, I don't understand how the sum of the two added vectors can have the same magnitude as the vector sum. A vector is defined as something with magnitude and direction, so vectors are equal if and only if they have the same magnitude and direction. The addition of vectors means combining two vectors, so the result of vector addition should give a vector with the same direction and magnitude as that of the combination of the added vectors, right? I can see how the sum of vectors A and B, if combined, would have the same direction as the third side of a triangle. What I don't understand here is how the magnitude of the third side can be equal to the magnitude of the other two sides. That would mean two sides of a triangle sum to the third side, wouldn't it?
Date: 11/14/2010 at 10:01:22 From: Doctor Ian Subject: Re: Why does the vector law of addition work? Hi David, Suppose you are standing on a giant grid. You are given two numbers (a,b). You move a units to the east, and b units to the north. Now you are given two more numbers (c,d). You move c units to the east, and d units to the north. What is the total distance you've moved to the east? It's a + c, right? And what is the total distance you've moved to the north? It's b + d, right? So you could have got to the same final point by being given the numbers (a + c, b + d) along with the same instructions. Does this make sense? Do you see how it illustrates the rule for vector addition? > A vector is defined as something with magnitude and direction, so > vectors are equal if and only if they have the same magnitude and > direction. The addition of vectors means combining two vectors, so the > result of vector addi