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

We will use the concept of vector subtraction in order to find the magnitude of |a - b|.

### Answer: Magnitude of the difference of vectors a and b, |a - b| is given by **√** (|a|^{2} + |b|^{2} - 2 |a| |b|) = **√** [c^{2} + d^{2} + m^{2} + n^{2} - 2 {**√** (c^{2} + d^{2}) **√** (m^{2} + n^{2})}].

Let us see how we will use the concept of vector subtraction in order to find the magnitude of |a - b|.

**Explanation**:

Let us suppose vector a = c i + d j and vector b = m i + n j

Magnitude of vector a, | a | = **√** (c^{2} + d^{2}) and magnitude of vector b, |b| = **√** (m^{2} + n^{2})

When vector b is subtracted from vector a then the magnitude of |a - b| is given by **√** (|a|^{2} + |b|^{2} - 2 |a| |b|).