# What is the value of the magnitude of the difference of vectors a and b, |a - b|?

**Solution:**

|a - b| = √(|a|^{2} + |b|^{2} - 2 a.b)

**Example:**

Let us consider two vectors. Let vector a = 2 i + 3 j and vector b = i - j

Let us determine the magnitude of the vectors.

Then, |a| = √(2^{2} +3^{2}) = √13

|b| = √(1^{2} +(-1)^{2}) = √2

Vector a - vector b = 2i - i + 3j +j = i + 4j

|i + 4j| = √(1^{2} + 4^{2}) = √17

a.b = (2×1) + (3× (-1)) = -1

Now substituting the values of |a|, |b| and a.b in √(|a|^{2} + |b|^{2} - 2 a.b)

√(|a|^{2} + |b|^{2} - 2 a.b) = √[ (√13)^{2}+(√2)^{2} - (2× (-1))] = √17

Thus, |a - b | = √(|a|^{2} + |b|^{2} - 2 a.b)

## What is the value of the magnitude of the difference of vectors a and b, |a - b|?

**Summary:**

The value of the magnitude of the difference of vectors a and b, |a - b| = √(|a|^{2} + |b|^{2} - 2 a.b)