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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

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Answer:

False.

Step-by-step 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-


a=3i+3j


b=3i-6j ,

then their resultant


r=b+a\\r=3i+3j+3i-6j\\r=6i-3j

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.

User Ravindra Ranwala
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