Vectors in $R^3$: Is $\begin{bmatrix}4\\3\\0\end{bmatrix}$ Valid?

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Thread starter bwpbruce
Start date Jan 1, 2015
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Vectors

In summary, a vector in $R^3$ is a mathematical object that represents a magnitude and direction in three-dimensional space. It is typically denoted by a column vector with three components, such as $\begin{bmatrix}x\\y\\z\end{bmatrix}$. These components can represent the magnitude and direction of the vector in three-dimensional space. A vector is considered valid in $R^3$ if it has three components and can be represented in three-dimensional space. To determine if a vector is valid in $R^3$, one must check if it has three components and use the Pythagorean theorem and trigonometric functions to determine its magnitude and direction.

Jan 1, 2015

bwpbruce

Is $\begin{bmatrix} 4 \\ 3 \\ 0 \end{bmatrix}$ in $R^3$?

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Jan 1, 2015

mathmari

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MHB

bwpbruce said:

Is $\begin{bmatrix} 4 \\ 3 \\ 0 \end{bmatrix}$ in $R^3$?

Yes, it is!

1. What is a vector in $R^3$?

A vector in $R^3$ is a mathematical object that represents a magnitude and direction in three-dimensional space. It is typically denoted by a column vector with three components, such as $\begin{bmatrix}x\\y\\z\end{bmatrix}$.

2. How is a vector in $R^3$ represented?

A vector in $R^3$ is typically represented by a column vector with three components, such as $\begin{bmatrix}x\\y\\z\end{bmatrix}$. These components can represent the magnitude and direction of the vector in three-dimensional space.

3. What does it mean for a vector to be valid in $R^3$?

A vector is considered valid in $R^3$ if it has three components and can be represented in three-dimensional space. This means that the vector must have a magnitude and direction that can be described using three numbers.

4. Is $\begin{bmatrix}4\\3\\0\end{bmatrix}$ a valid vector in $R^3$?

Yes, $\begin{bmatrix}4\\3\\0\end{bmatrix}$ is a valid vector in $R^3$. It has three components and can be represented in three-dimensional space with a magnitude of 5 and a direction of 53.13 degrees from the positive x-axis.

5. How can I determine if a vector is valid in $R^3$?

To determine if a vector is valid in $R^3$, you must first check if it has three components. Then, you can use the Pythagorean theorem and trigonometric functions to determine the magnitude and direction of the vector. If these values can be represented in three-dimensional space, then the vector is considered valid in $R^3$.