Vector addition and Pythagorean theoremFinding length or magnitude using vector addition and the Pythagorean theorem.I...

Grimanijd

Grimanijd

Answered

2022-07-05

Vector addition and Pythagorean theorem
Finding length or magnitude using vector addition and the Pythagorean theorem.
I am trying to understand why vector addition and the Pythagorean theorem are giving different results?

Vector Addition :
According to diagram (A) : a + b = c now suppose : magnitude of a = 3, magnitude of b = 4 then
c = a + b
c = 3 + 4
magnitude of c = 7
Pythagorean Theorem
Now when we consider this as a triangle shown in diagram (B)
Similarly, length of a=3, length of b=4
so according to Pythagorean theorem
hypotenuse 2 = opposite 2 + adjacent 2
c 2 = a 2 + b 2 i.e.
c 2 = 3 2 + 4 2
c = 9 + 16 = 25
length of c = 5
Why there is inconsistency in the results? I am doing something wrong?
Thanks!

Answer & Explanation

Jamiya Costa

Jamiya Costa

Expert

2022-07-06Added 18 answers

The magnitude of a vector ( a + b ) is obtained in a similar way to that for Pythagorean triangles. It is incorrect to simply add up magnitudes of a and b .
Rather, c = a + b

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