Question

refer to the figure below to answer the following questions. which of the displacements, when added in the order given, will yield a displacement equal to d1 + d2 + d3? d2 + d4 + d3 d4 + d3 + d1 d2 + d1 + d3 d3 + d4 + d1 question 4 in the figure above, which diagram represents the vector addition c = a + b? iv iii i ii

Explanation:

Step1: Recall vector - addition rules

Vector addition is commutative, but we need to follow the order of addition as given. For vectors, when adding them, the tail of the next vector is placed at the head of the previous vector.

Step2: Analyze the first problem

We want to find which combination of displacements gives $d_1 + d_2 + d_3$. By the rules of vector addition, we need to add the vectors in the order that matches the sequence of displacements. Starting with $d_1$, then adding $d_2$ (placing the tail of $d_2$ at the head of $d_1$), and then adding $d_3$ (placing the tail of $d_3$ at the head of $d_2$). The correct order is $d_2 + d_1 + d_3$ because when we start with $d_2$, then add $d_1$ (which will be in the correct relative position), and then add $d_3$.

Step3: Analyze the second problem

For vector addition $C = A + B$, using the head - to - tail method, we place the tail of vector $B$ at the head of vector $A$. The resultant vector $C$ goes from the tail of $A$ to the head of $B$. In diagram I, the tail of $B$ is placed at the head of $A$ and the resultant vector $C$ is drawn from the tail of $A$ to the head of $B$.

Answer:

1. $d_2 + d_1 + d_3$
2. I