Question

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

Answer 1

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-

$a=3i+3j$

$b=3i-6j$ ,

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.