Question

Vector A has a magnitude of 74 units and points west, while vector B has the same magnitude and points due south. Find the magnitude and direction of a) A + B and b) A - B. Specify the directions relative due west.​

Answer 1

Answer:here is your answer

Step-by-step explanation:

a) The magnitude and direction of the sum of two vectors can be found by using the Pythagorean theorem and the concept of angles. If we consider A and B to be the components of the sum vector, then the sum vector can be represented as follows:

A + B = (74 units, West) + (74 units, South) = √(74^2 + 74^2) units, arctan(74/74) = 106 units, arctan(1) = 45° South of West

So, the magnitude of A + B is 106 units and the direction is 45° South of West.

b) The magnitude and direction of the difference of two vectors can be found similarly. If we consider A and B to be the components of the difference vector, then the difference vector can be represented as follows:

A - B = (74 units, West) - (74 units, South) = √(74^2 + 74^2) units, arctan(-74/74) = 106 units, arctan(-1) = 45° North of West

So, the magnitude of A - B is 106 units and the direction is 45° North of West.