Dot product Transitional Reasoning Practice

Questions

1. 1.

   In a physics modeling activity, a student evaluates two coplanar displacement vectors, $\vec{A} = (4\hat{i} - 2\hat{j})\text{ m}$ and $\vec{B} = (2\hat{i} + 5\hat{j})\text{ m}$, to determine their relative orientation. The student computes their scalar (dot) product $\vec{A} \cdot \vec{B}$ to classify the angle $\theta$ between them. What is the value of $\vec{A} \cdot \vec{B}$, and what does this result indicate about $\theta$?

   • A) $+18\text{ m}^2$, indicating that $\theta$ is acute
   • B) $-2\text{ m}^2$, indicating that $\theta$ is acute
   • C) $-2\text{ m}^2$, indicating that $\theta$ is obtuse
   • D) $+8\text{ m}^2$, indicating that $\theta$ is obtuse

Answers and step-by-step solutions appear after you finish the test.