Question

Can a vector have a component equal to zero and still have nonzero magnitude?

a) Yes
b) No

Answer 1

Yes, a vector can have a component equal to zero and still have a nonzero magnitude.

Step-by-step explanation:

Yes, a vector can have a component equal to zero and still have a nonzero magnitude. The magnitude of a vector is determined by the Pythagorean theorem, which involves the squares of its components. Therefore, even if one of the components is zero, the other components can still have nonzero values, resulting in a nonzero magnitude.

For example, consider a 2-dimensional vector with its x-component equal to zero and its y-component equal to 3. The magnitude of this vector is √(0^2 + 3^2) = 3, which is nonzero.