Question

Given the components of vectors A and B are:

Aₓ=+7.6, A_z=-9.2
Bₓ=-3.8, B_z=4.6

The relationship between two vectors can be defined through their components. Let's compare the x and z components separately to determine the relationship between vector A and vector B.

A. B=-0.5A
B. B=A-(2.0)
C. B=A-(3.8,-7.6)
D. None of the above

Answer 1

The relationship between vectors A and B is determined through their components. By subtracting vector B's components from vector A's components, B can be expressed as A subtracting a vector with components (3.8, 7.6), so the correct answer is option C.

Step-by-step explanation:

The question asks us to compare the components of vectors A and B and determine the relationship between them. By using the concept of vector subtraction, we can compare the components of vector A with vector B. Since vector subtraction is accomplished by adding the opposite of vector B (-B) to vector A, we find the components of -B by taking the negatives of the components of B. Therefore, the relationship between vectors A and B through their components can be formulated as follows:

• Ax - Bx = 7.6 - (-3.8) = 7.6 + 3.8 = 11.4
• Az - Bz = -9.2 - (4.6) = -9.2 - 4.6 = -13.8

This implies that the vector B can be expressed as a transformation of A, subtracting a vector with components (3.8, 7.6), meaning the correct relationship is B = A - (3.8, 7.6). Therefore, the correct answer is option C.