Question

What from the following list of statements about vectors is definitely true? (section 3.3) The magnitude of a vector can be smaller than length of one of its components. Magnitude of a vector is positive if it is directed in +x and negative if is is directed in -X direction. Magnitude of a vector can be zero if only one of components is zero. If vector A has bigger component along x direction than vector B, it immediately means, the vector A has bigger magnitude than vector B. Magnitude of a vector can be zero only if all components of a vector are zero.

Answer 1

"Magnitude of a vector can be zero only if all components of a vector are zero."

Step-by-step explanation:

"The magnitude of a vector can be smaller than length of one of its components."

Wrong, the magnitude of a vector is at least equal to the length of a component. This is because of the Pythagoras theorem. It can never be smaller.

"Magnitude of a vector is positive if it is directed in +x and negative if is is directed in -X direction."

False. Magnitude of a vector is always positive.

"Magnitude of a vector can be zero if only one of components is zero."

Wrong. For the magnitude of a vector to be zero, all components must be zero.

"If vector A has bigger component along x direction than vector B, it immediately means, the vector A has bigger magnitude than vector B."

Wrong. The magnitude of a vector depends on all components, not only the X component.

"Magnitude of a vector can be zero only if all components of a vector are zero."

True.