4. Which of the following is an accurate statement about vectors?
A. Rotating a vector about an axis passing through the tip of the vector does not change the vector(definitely not right)
B. The magnitude of a vector can be zero even if one of its components is not zero.(this ones not right either)
C. If two vectors have unequal magnitudes, it is possible that their vector sum is zero.
D. It is possible to add a scalar quantity to a vector(not right)
E. The magnitude of a vector may be positive even if all of its compenets are negative.
V = -1 i - 2 j
magnitude = sqrt (1+4) = sqrt 5
which is +
You could do C with 3 vectors, but I think not with 2.
To find the accurate statement about vectors, let's analyze each of the options:
A. Rotating a vector about an axis passing through the tip of the vector does not change the vector. This statement is not accurate because rotating a vector will change its direction, thus changing the vector itself.
B. The magnitude of a vector can be zero even if one of its components is not zero. This statement is also not accurate. The magnitude of a vector is determined by the combination of its components, so if any component is non-zero, the magnitude cannot be zero.
C. If two vectors have unequal magnitudes, it is possible that their vector sum is zero. This statement is accurate. The vector sum of two vectors can result in zero if their magnitudes and directions are appropriately balanced. This is known as vector cancellation.
D. It is possible to add a scalar quantity to a vector. This statement is not accurate. Scalar quantities only have magnitude and no direction, while vectors have both magnitude and direction. Adding a scalar quantity to a vector does not result in a valid vector sum.
E. The magnitude of a vector may be positive even if all of its components are negative. This statement is accurate. The sign of the components of a vector only determines its direction, while the magnitude represents the absolute value or size of the vector. Therefore, a vector can have negative components but still have a positive magnitude.
Therefore, the accurate statement about vectors is:
C. If two vectors have unequal magnitudes, it is possible that their vector sum is zero.