contestada

Since vectors always have positive magnitudes, the sum of two vectors must have a magnitude greater than the magnitude of either one of them. O True O False

Respuesta :

Answer:

False.

Explanation:

Yes the magnitude of a vector is always positive , but a vector consists of

  • magnitude
  • direction

when two vectors are added their direction may be opposite to each other For example-

[tex]a=3i+3j[/tex]

[tex]b=3i-6j[/tex] ,

then their resultant

[tex]r=b+a\\r=3i+3j+3i-6j\\r=6i-3j[/tex]

This resultant vector's x and y component equal to y and x component of vector b so its magnitude will be equal to magnitude of vector b.

Therefore, the resultant magnitude not necessary equal to the magnitude of either vector.

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