Question

Which of the following statements about the three vectors in Figure 1.24 are correct? $\mathbf{\left(}\mathit{a}\mathbf{\right)}\mathbf{}\overrightarrow{\mathbf{s}}\mathbf{=}\overrightarrow{\mathbf{t}}\mathbf{-}\overrightarrow{\mathbf{r}}\mathbf{}\mathbf{\left(}\mathit{b}\mathbf{\right)}\mathbf{}\overrightarrow{\mathbf{r}}\mathbf{=}\overrightarrow{\mathbf{t}}\mathbf{-}\overrightarrow{\mathbf{s}}\mathbf{}\mathbf{\left(}\mathit{c}\mathbf{\right)}\mathbf{}\overrightarrow{\mathbf{r}}\mathbf{+}\overrightarrow{\mathbf{t}}\mathbf{=}\overrightarrow{\mathbf{s}}\mathbf{}\mathbf{\left(}\mathit{d}\mathbf{\right)}\mathbf{}\mathbf{}\overrightarrow{\mathbf{s}}\mathbf{+}\overrightarrow{\mathbf{t}}\mathbf{=}\overrightarrow{\mathbf{r}}\mathbf{\left(}\mathit{e}\mathbf{\right)}\mathbf{}\mathbf{}\overrightarrow{\mathbf{r}}\mathbf{+}\overrightarrow{\mathbf{s}}\mathbf{=}\overrightarrow{\mathbf{t}}$

Short answer

Based on given figure, (a), (b) and (e) are correct statements.

Step-by-step solution

Definition of Law of vector addition

When two vectors are represented by two sides of a triangle with the same order of magnitude and direction, the magnitude and direction of the resultant vector is represented by the third side of the triangle.

Correct equation according to given figure

Based on the given figure$\overrightarrow{r}+\overrightarrow{s}=\overrightarrow{t}$, on applying the law of vector addition, vector addition equation can be expressed as .

Analyzing statement (a)

(a)

The correct vector addition equation according to the given figure is $\overrightarrow{r}+\overrightarrow{s}=\overrightarrow{t}$.

This equation can also be expressed as $\overrightarrow{s}=\overrightarrow{t}-\overrightarrow{r}$, which is the given equation in this part. Hence, it is a correct statement.

Analyzing statement (b)

(b)

The correct vector addition equation according to the given figure is $\overrightarrow{r}+\overrightarrow{s}=\overrightarrow{t}$. This equation can also be expressed as role="math" localid="1657082735741" $\overrightarrow{r}=\overrightarrow{t}-\overrightarrow{s}$, which is the given equation in this part. Hence, it is a correct statement.

Analyzing statement (c)

(c)

The correct vector addition equation according to the given figure is $\overrightarrow{r}+\overrightarrow{s}=\overrightarrow{t}$. This equation cannot be expressed as $\overrightarrow{r}+\overrightarrow{t}=\overrightarrow{s}$. Hence, the given statement is incorrect.

Analyzing statement (d)

(d)

The correct vector addition equation according to the given figure is $\overrightarrow{r}+\overrightarrow{s}=\overrightarrow{t}$. This equation cannot be expressed as $\overrightarrow{s}+\overrightarrow{t}=\overrightarrow{r}$.Hence, the given statement is incorrect.

Analyzing statement (e)

(e)

The correct vector addition equation according to the given figure is$\overrightarrow{r}+\overrightarrow{s}=\overrightarrow{t}$, which is same as the given equation in this part. Hence, it is a correct statement.

Therefore, based on vector law of addition, (a), (b) and (e) are correct statements.