What process involves numerically adding vectors by using Pythagoras' theorem to calculate magnitude and direction?

What process involves numerically adding vectors by using Pythagoras' theorem to calculate magnitude and direction?

• A. Vector addition
• B. Vector subtraction
• C. Vector resolution
• D. Vector transformation

Answer: (A)

The process of numerically adding vectors using Pythagoras' theorem to calculate both magnitude and direction is known as vector addition. When two vectors are represented graphically, they can be added by placing the tail of one vector at the head of the other. To find the resultant vector's magnitude and direction, the right triangle formed by the two vectors can be analyzed with Pythagoras' theorem. The magnitude of the resultant is the hypotenuse of this right triangle, calculated using the formula \( R = \sqrt{A^2 + B^2} \) for vectors A and B. The direction can be determined using trigonometric functions, typically by calculating the angle with respect to a specific axis using the sine or cosine ratios. In contrast, vector subtraction involves finding the difference between two vectors, vector resolution refers to breaking a vector into its components, and vector transformation deals with changing vectors based on various operations but does not directly relate to the addition process outlined in this question.

The process of numerically adding vectors using Pythagoras' theorem to calculate both magnitude and direction is known as vector addition. When two vectors are represented graphically, they can be added by placing the tail of one vector at the head of the other. To find the resultant vector's magnitude and direction, the right triangle formed by the two vectors can be analyzed with Pythagoras' theorem. The magnitude of the resultant is the hypotenuse of this right triangle, calculated using the formula ( R = \sqrt{A^2 + B^2} ) for vectors A and B. The direction can be determined using trigonometric functions, typically by calculating the angle with respect to a specific axis using the sine or cosine ratios.

In contrast, vector subtraction involves finding the difference between two vectors, vector resolution refers to breaking a vector into its components, and vector transformation deals with changing vectors based on various operations but does not directly relate to the addition process outlined in this question.