Chapter 12.6, Problem 45PPSE

Solution

To find: The explain the vector and its role in vector addition.

The zero vector acts as an additive identity in vectors because adding zero vector to any vector results in the same vector.

Given information:

Given, when any vector is subtracted from itself, the result is still a vector but a unique one.

Calculation:

Consider a vector $〈a,b〉$

Subtracting the vector from itself:

  $〈a,b〉-〈a,b〉=〈0,0〉$

This vector is known as the zero vector. It is unique since every vector has a magnitude and direction. But the zero vector has a magnitude of 0 and the direction is undefined.

The zero vector acts as an additive identity in vectors because adding zero vector to any vector results in the same vector.

Conclusion:

The zero vector acts as an additive identity in vectors because adding zero vector to any vector results in the same vector.