Question

Vector $\overrightarrow{A}$has a magnitude of 29units and points y direction. When vector $\overrightarrow{B}$ is added to$\overrightarrow{A}$the resultant vector $\overrightarrow{A}+\overrightarrow{B}$points in the negative ydirection with a magnitude of 14units. Find the magnitude and direction of $\overrightarrow{B}$.

Short answer

The magnitude of $\overrightarrow{B}=43$ and the direction of B is along the negative y axis.

Step-by-step solution

Define vector

A vector is a quantity that has both a direction and a magnitude, and is used to determine the relative location of two points in space.

State given data

We are given that $R⃗=A⃗+B⃗$, when two vectors are added graphically, the second vector positioned with its tail at the trip of first vector.

width="111">A⃗=+29jA⃗+B⃗=-14j

Step 3: Find the magnitude and direction of B→

$$\begin{gathered} \overrightarrow{A}=0i+29j=+29j \\ \overrightarrow{A}+\overrightarrow{B}=0i-14j=-14j \\ \overrightarrow{B}=-14j-29j=-43j \end{gathered}$$

So, the magnitude of$\overrightarrow{B}=43$and the direction of B is along the negative y axis.