Question

1 mark for review an object is located at a position a distance d from the origin at an angle θ as shown in the diagram. what is the position of the object expressed in unit - vector notation? a -dcosθî + dsinθĵ b dcosθî - dsinθĵ c -dsinθî + dcosθĵ d dsinθî - dcosθĵ

Explanation:

Step1: Recall vector - component formula

The x - component of a vector $\vec{R}$ with magnitude $R$ and angle $\theta$ with the x - axis is $R_x=-R\sin\theta$ (negative x - direction) and the y - component is $R_y = R\cos\theta$ (positive y - direction).

Step2: Write in unit - vector notation

The position vector $\vec{r}$ in unit - vector notation is $\vec{r}=R_x\hat{i}+R_y\hat{j}$. Substituting $R = D$, we get $\vec{r}=-D\sin\theta\hat{i}+D\cos\theta\hat{j}$.

Answer:

C. $-D\sin\theta\hat{i}+D\cos\theta\hat{j}$