Vector addition and Pythagorean theoremFinding 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 + 4magnitude of c = 7Pythagorean TheoremNow when we consider this as a triangle shown in diagram (B)Similarly, length of a=3, length of b=4so 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 = 5Why there is inconsistency in the results? I am doing something wrong?Thanks!

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Vector addition and Pythagorean theoremFinding 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  +  4magnitude of c = 7Pythagorean TheoremNow when we consider this as a triangle shown in diagram (B)Similarly, length of a=3, length of b=4so 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 = 5Why there is inconsistency in the results? I am doing something wrong?Thanks!

Jamiya Costa · Accepted Answer

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        →              ‖

Vector addition and Pythagorean theorem Finding length or magnitude using vector addition and the P

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