Which of the following is an accurate statement?
a) a vector cannot have zero magnitude if one of its components is not zero
b) the magnitude of a vector can be less than the magnitude of one of its componenets
c) if the magnitude of vector A is less than the magnitude of vector B, then the x-compnent of A is less than the x-componnent of B
d) the magnitude of a vector can be postitive or negative
I know that a) is wrong, i think c) is the correct answer since if you use V= v_0*cos (theda) it would be valid
Consider b) vector1 is 24@270 and vector2 is 24@080.
To determine which statement is accurate, let's analyze each option:
a) "A vector cannot have zero magnitude if one of its components is not zero."
This statement is incorrect. The magnitude of a vector can still be zero even if one of its components is not zero. For example, if we have a vector with components (0, 5), its magnitude is √(0^2 + 5^2) = 5.
b) "The magnitude of a vector can be less than the magnitude of one of its components."
This statement is accurate. The magnitude of a vector represents its overall length or magnitude in space. It is possible for the magnitude of a vector to be smaller than the magnitude of one of its components. For example, if we have a vector with components (3, 4), the magnitude is √(3^2 + 4^2) = 5, which is smaller than the magnitude of the component 4.
c) "If the magnitude of vector A is less than the magnitude of vector B, then the x-component of A is less than the x-component of B."
This statement is incorrect. The magnitude of a vector is related to the overall length or magnitude of the vector and does not directly determine the individual components. Therefore, the x-component of vector A could still be greater than the x-component of vector B, even if the magnitude of A is less than the magnitude of B.
d) "The magnitude of a vector can be positive or negative."
This statement is incorrect. The magnitude of a vector is always a positive value as it represents the length or magnitude of the vector in space. The sign of a vector is associated with its individual components, but the magnitude itself is always positive.
Based on the analysis above, the accurate statement is:
b) "The magnitude of a vector can be less than the magnitude of one of its components."