Questions: Vector A has components Ax=1.40 cm, Ay=2.15 cm; vector B has components Bx=4.20 cm, By=-3.76 cm. Find the components of the vector difference B-A. Express your answers in centimeters separated by a comma. (B-A)x,(B-A)y=

Vector A has components Ax=1.40 cm, Ay=2.15 cm; vector B has components Bx=4.20 cm, By=-3.76 cm.

Find the components of the vector difference B-A.
Express your answers in centimeters separated by a comma.
(B-A)x,(B-A)y=

Transcript text: Vector $\vec{A}$ has components $A_{x}=1.40 \mathrm{~cm}, A_{y}=2.15 \mathrm{~cm}$; vector $\vec{B}$ has components $B_{x}=4.20 \mathrm{~cm}, B_{y}=-3.76 \mathrm{~cm}$. Find the components of the vector difference $\vec{B}-\vec{A}$. Express your answers in centimeters separated by a comma. \[ (\vec{B}-\vec{A})_{x},(\vec{B}-\vec{A})_{y}= \]

Solution

Solution Steps

Step 1: Determine the Components of Vector Difference

To find the components of the vector difference $\vec{B} - \vec{A}$, we subtract the components of $\vec{A}$ from the components of $\vec{B}$.

Step 2: Calculate the x-component

The x-component of $\vec{B} - \vec{A}$ is calculated as follows: \[ (\vec{B} - \vec{A})_x = B_x - A_x = 4.20 \, \text{cm} - 1.40 \, \text{cm} = 2.80 \, \text{cm} \]

Step 3: Calculate the y-component

The y-component of $\vec{B} - \vec{A}$ is calculated as follows: \[ (\vec{B} - \vec{A})_y = B_y - A_y = -3.76 \, \text{cm} - 2.15 \, \text{cm} = -5.91 \, \text{cm} \]