Answer to Question #100543 in Geometry for Felix

Question #100543
Show that if a and b are
(a) in the same direction then |a + b| = |a| + |b|,
(b) in the opposite direction then |a − b| = |a| + |b|.
1
Expert's answer
2019-12-17T10:03:57-0500

If there are two vectors of magnitude a and b then their resultant magnitude is written by

(a2 + b2 + 2abcos"\\theta")1/2 where θ is the angle between the two vectors


a) when a and b are in the same direction

θ =00 and as cos00=1

then magnitude of two vectors become "\\vert a+b \\vert=" (a2+b2+2ab)1/2=

=(a+b) = |a| + |b|


b) when a and b are in the opposite direction

θ =1800 and as cos1800=-1

then magnitude of two vectors become "\\vert a-b \\vert=" (a2+b2-2ab)1/2=

=(a-b) = |a| - |b|




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