If the resultant vector of the sum of three vectors is zero,the three vectors must have the following property. A)The sum of each component of the three vectors is zero. B)The sum of any two vectors is the negative of the third vector. C)All three vectors lie in the same plane. D)The magnitude of the sum of any two vectors is equal to the magnitude of the third vector. E)All the above are correct.

Question

Quizplus · Accepted Answer

For the resultant vector to be zero, the three vectors must cancel each other out. This means that their components must add up to zero (option A), and the sum of any two vectors must be the negative of the third vector (option B).

Additionally, if the vectors are arranged tail-to-tip, they must lie in the same plane (option C) in order for their sum to be zero.

Finally, if we take any two vectors, say A and B, then the magnitude of their sum must be equal to the magnitude of the third vector (option D). This is because the three vectors form a triangle, and in a triangle, each side is equal to the sum of the other two sides minus twice their vector sum. Thus, we have ||A+B|| = ||C||, ||A+C|| = ||B||, and ||B+C|| = ||A||.

Therefore, all of the above options are correct.

If the Resultant Vector of the Sum of Three Vectors