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| = √(2² +3²) = √13

|b| = √(1² +(-1)²) = √2

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

|i + 4j| = √(1² + 4²) = √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)