Question

In Active Example 2.6, suppose that you want to redesign the truss, changing the position of point $D$ so that the magnitude of the vector $\mathbf{r}_{C D}$ from point $C$ to point $D$ is $3 \mathrm{~m}$. To accomplish this, let the coordinates of point $D$ be $\left(2, y_D, 1\right) \mathrm{m}$, and determine the value of $y_D$ so that $\left|\mathbf{r}_{C D}\right|=3 \mathrm{~m}$. Draw a sketch of the truss with point $D$ in its new position. What are the new direction cosines of $\mathbf{r}_{C D}$ ?

Name: Problem 67, Chapter 2: Engineering Mechanics: Statics
Uploaded: 2021-01-26T14:47:50-08:00
Duration: 4 min 15 s
Channel: Rashmi Sinha

   In Active Example 2.6, suppose that you want to redesign the truss, changing the position of point $D$ so that the magnitude of the vector $\mathbf{r}_{C D}$ from point $C$ to point $D$ is $3 \mathrm{~m}$. To accomplish this, let the coordinates of point $D$ be $\left(2, y_D, 1\right) \mathrm{m}$, and determine the value of $y_D$ so that $\left|\mathbf{r}_{C D}\right|=3 \mathrm{~m}$. Draw a sketch of the truss with point $D$ in its new position. What are the new direction cosines of $\mathbf{r}_{C D}$ ?

Engineering Mechanics: Statics

Anthony M. Bedford,… 5th Edition

Chapter 2, Problem 67

Instant Answer

Solved by Expert Rashmi Sinha

01/26/2021

Step 1

From the problem, we know that point $ C $ has coordinates $ (0, 0, 0) $ and point $ D $ has coordinates $ (2, y_D, 1) $. Show more…

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In Active Example 2.6, suppose that you want to redesign the truss, changing the position of point $D$ so that the magnitude of the vector $\mathbf{r}_{C D}$ from point $C$ to point $D$ is $3 \mathrm{~m}$. To accomplish this, let the coordinates of point $D$ be $\left(2, y_D, 1\right) \mathrm{m}$, and determine the value of $y_D$ so that $\left|\mathbf{r}_{C D}\right|=3 \mathrm{~m}$. Draw a sketch of the truss with point $D$ in its new position. What are the new direction cosines of $\mathbf{r}_{C D}$ ?

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Key Concepts

Coordinate Geometry in Three Dimensions

This concept refers to the representation and analysis of geometric figures and points in three-dimensional space using coordinates. It provides the framework for describing positions, computing distances, and performing transformations, which are essential for designing structures and analyzing their spatial properties.

Vector Magnitude

This concept involves calculating the length of a vector in a coordinate space. In three dimensions, the magnitude is determined by taking the square root of the sum of the squares of its components. It is a fundamental concept in vector algebra and is used to measure the size or length of any vector.

Direction Cosines

Direction cosines are the cosines of the angles between a vector and the coordinate axes. They are obtained by dividing the vector's individual components by its magnitude, thus providing a normalized measure of the vector's orientation in space.

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