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#### Concept explainers

Can the sum of the magnitudes of two vectors ever be equal to the magnitude of the sum of the same two vectors? If no, why not? If yes, when?

**To prove:**

The sum of the magnitudes of two vectors are be equal to the magnitude of the sum of the same two vectors.

## Answer to Problem 1Q

**Solution:**

Yes, when two vectors are in same direction then the sum of the magnitudes of two vectors are equal to the magnitude of the sum of the same two vectors.

### Explanation of Solution

We can use formula of the addition of two vectors and find their magnitudes.

**Formula:**

**Calculations:**

Consider

**The sum of the magnitude of two vectors**:

** The magnitude of the sum of two vectors:**

According to the vector addition law,

Hence, two vectors are acting in the same direction, then

**Conclusion:**

We can use expression of vector addition law and find their magnitudes. It indicates that the sum of the magnitudes of two vectors can be equal to the magnitude of the sum of the same two vectors when they are going along the same direction.

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# Chapter 3 Solutions

FUNDAMENTALS OF PHYSICS - EXTENDED

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- If two vectors are equal, what can you say about their components? What can you say about their magnitudes? What can you say about their directions?
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