Given 2 vectors A = 4.00i + 3.00j and B = 5.00i - 2.00 j how do you find the magnitude and direction of the vector difference A - B?

Solution:

Given A = 4.00i + 3.00j and B = 5.00i - 2.00 j

The difference of two vectors can be calculated as difference between in individual directions

A - B = (4.00i + 3.00j) - (5.00i - 2.00 j)

A - B = 4.00i - 5.00i + 3.00j - (-2.00j)

A - B = -1.00i + 3.00j + 2.00j

A - B = -1.00i + 5.00j

Therefore, the direction of A-B is -1.00i + 5.00j

The magnitude of A vector is expressed as √(a² + b²)

Magnitude: |A - B| = √ ((-1)² + 5²) = √1 + 25 = √26

Given 2 vectors A = 4.00i + 3.00j and B = 5.00i - 2.00 j how do you find the magnitude and direction of the vector difference A - B?

Summary:

Given 2 vectors A = 4.00i + 3.00j and B = 5.00i - 2.00 j, the magnitude and direction of the vector difference A - B are -1.00i + 5.00j and √26 respectively.