Question

The components of vector A and vector B are:

[ A_x = +7.6 quad B_x = -15.2 ]
[ A_y = -9.2 quad B_y = -18.4 ]

Which equation describes the relationship between the two vectors?
A. ( mathbf(OB) = 2mathbf(OB) )
B. ( mathbf(OB) = mathbf(A) - (2.0) )
C. ( mathbf(OB) = 16 mathbf(A) )
D. ( mathbf(AB) = mathbf(A) )

Answer 1

The equation that describes the relationship between vector OB (vector from the origin to point B) and vectors A and B is D. OB = A - B.

Step-by-step explanation:

To determine the relationship between vectors A, B, and OB, we need to consider vector addition. The vector OB is the vector from the origin to point B, and it can be represented as the difference between vectors A and B (i.e., OB = A - B).

Breaking this down component-wise, Oᵦₓ = Aₓ - Bₓ and Oᵦᵧ = Aᵧ - Bᵧ. Substituting the given values, we have Oᵦₓ = 7.6 - (-15.2) = 22.8 and Oᵦᵧ = -9.2 - (-18.4) = 9.2, which corresponds to the components of OB.

Therefore, the correct equation describing the relationship between vectors A, B, and OB is OB = A - B, making the final answer option D.

In summary, the vector OB is formed by subtracting vector B from vector A, and the components of OB are calculated by subtracting the corresponding components of B from those of A.