Which of the following is an accurate statement about vectors? It is possible to add a scalar quantity to a vector. If two vectors have unequal magnitudes, it is possible that their vector sum is zero. Rotating a vector about an axis passing through the tip of the vector does not change the vector. The magnitude of a vector can be zero even if one of its components is not zero. The magnitude of a vector may be positive even if all of its components are negative.

The magnitude of a vector may be positive even if all of its components are negative.
In fact, the length of a vector is calculated as
lvl = root ((a) ^ 2 + (b) ^ 2)
Where a and b are components of the vector, both can be less than zero, however the result of the magnitude of the vector is positive.
answer:
The magnitude of a vector may be positive even if all of its components are negative.

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Kalahira Kalahira · Answer 2 · 2018-02-08T21:17:28+01:00

Let's take a look at the statements and see what makes sense about vectors.

It is possible to add a scalar quantity to a vector.
* False. Try to add a scalar to a vector. How would you do it? Pick an axis and add to that? Which axis? So this is a bad choice.

If two vectors have unequal magnitudes, it is possible that their vector sum is zero.
* False. Imagine standing at in the middle of a football field, picking a direction at random, and then stepping off 15 yards in a straight line. Now from that new point, try to get back to your starting point by moving in any direction you desire for 10 yards. That's not gonna happen. And for the same reason, this is a bad choice.

Rotating a vector about an axis passing through the tip of the vector does not change the vector.
* A vector has 2 components, direction and magnitude. And the rotation changes the direction and therefore the vector. So this is a bad choice.

The magnitude of a vector can be zero even if one of its components is not zero.
* The magnitude of a vectors is the positive square root of the sum of the squares of all its components. That "square of its components" will always be a non-zero positive value if the component is non-zero. And since all the squares will be either 0 or positive, then if any component is non-zero, the sum will be positive. And hence the square root will be positive. And hence non-zero. So this is a bad choice.

The magnitude of a vector may be positive even if all of its components are negative.
* Quite true. Take note in the above option about the magnitude being the square root of the sum of the squares. The result will be either 0 or positive. And if any component is non-zero, then the magnitude will be a positive value.