What must be true for two vectors to add up to ZERO? Choose all that apply.

1)Their y-components must be equal.
2)They must be anti-parallel (point in opposite directions).
3) Their x-components must be equal.
4)They must be parallel (point in the same direction).
5) They must have equal magnitudes.
6) They must have opposite magnitudes

2 and 5

I will be happy to critique your thinking.

What is wrong with 1 and 3?

What is wrong with 6 ?

All of the following apply: 1 ,2 , 3 ,

5 , 6.

No Henry, for example in #1 the components must be opposite, not equal.

To determine what must be true for two vectors to add up to zero, let's examine the concept of vector addition.

Vector addition is a mathematical operation in which two vectors are combined to form a resultant vector. The resultant vector represents the sum of the two vectors.

When two vectors are added together, their components are added separately. The x-component of the resultant vector is the sum of the x-components of the two vectors being added, and the y-component is the sum of their y-components.

For two vectors to add up to zero, the sum of their x-components and the sum of their y-components must both equal zero. Therefore, the following statements must be true:

3) Their x-components must be equal.
1) Their y-components must be equal.

This means that the x-component of one vector should have the same magnitude but the opposite sign of the other vector's x-component. Similarly, the y-component of one vector should have the same magnitude but the opposite sign of the other vector's y-component.

Additionally, for two vectors to add up to zero, they must be anti-parallel, meaning they point in opposite directions (statement 2).

Therefore, the correct answers are:

1) Their y-components must be equal.
2) They must be anti-parallel (point in opposite directions).
3) Their x-components must be equal.