Question

Which relationships hold true for the sum of the magnitudes of vectors u and v, which are perpendicular? Select all correct answers.


`||u+v||=||u||+||v||\\||u+v||=√(||u||^2+||v||^2)\\||u+v||\ \textless \ √(||u||^2+||v||^2)\\||u+v||\ \textless \ ||u||+||v||`

Answer 1

As with any right triangle, the length of the hypotenuse is equal to the root of the sum of the squares of the legs. That root is less than the sum of the leg lengths and greater than the longest leg (for non-zero leg lengths).

_____

Comment on the choices

The relationship is actually ...

║u+v║ ≤ ║u║ + ║v║

That makes the first selection possibly correct. It will only be correct if ║u║ or ║v║ is zero. The problem statement does not rule out that case.

Explanation:

Answer 2

the correct answers are marked in green below

Explanation:

As with any right triangle, the length of the hypotenuse is equal to the root of the sum of the squares of the legs. That root is less than the sum of the leg lengths and greater than the longest leg (for non-zero leg lengths).

_____

Comment on the choices

The relationship is actually ...

║u+v║ ≤ ║u║ + ║v║

That makes the first selection possibly correct. It will only be correct if ║u║ or ║v║ is zero. The problem statement does not rule out that case.