### Orthogonal Projection Problem**Problem Statement:**Compute the orthogonal projection of $\begin{bmatrix} -1 \\ 4 \end{bmatrix}$ onto the line through $\begin{bmatrix} -3 \\ 5 \end{bmatrix}$ and the origin.**Solution:**The orthogonal projection is $\begin{bmatrix} \boxed{} \\ \boxed{} \end{bmatrix}$.Enter your answer in the edit fields and then click "Check Answer."**Note:**For computing the orthogonal projection of a vector $\mathbf{a}$ onto another vector $\mathbf{b}$, use the formula:\[\text{proj}_{\mathbf{b}} \mathbf{a} = \frac{\mathbf{a} \cdot \mathbf{b}}{\mathbf{b} \cdot \mathbf{b}} \mathbf{b}\]where $\mathbf{a} \cdot \mathbf{b}$ is the dot product of vectors $\mathbf{a}$ and $\mathbf{b}$. ### Instructions:1. Calculate the dot product of the vectors.2. Find the magnitude squared of vector $\mathbf{b}$.3. Use the projection formula to find the result.4. Fill in the boxes provided with the correct values.**Diagram and Explanation:**(In this case, there are no diagrams provided. An explanation of steps and formulae is included above.)After computing, enter your answers and click "Check Answer" to verify.### Example Calculation:Given:$\mathbf{a} = \begin{bmatrix} -1 \\ 4 \end{bmatrix}, \mathbf{b} = \begin{bmatrix} -3 \\ 5 \end{bmatrix}$1. Compute the dot product $\mathbf{a} \cdot \mathbf{b}$:\[\mathbf{a} \cdot \mathbf{b} = (-1)(-3) + (4)(5) = 3 + 20 = 23\]2. Compute $\mathbf{b} \cdot \mathbf{b}$:\[\mathbf{b} \cdot \mathbf{b} = (-3)^2 + 5^2 = 9 + 25 = 34\]3. Use the projection

Answered: Image /qna-images/answer/1723bb22-aea6-4891-b68b-ef7a11ba91be.jpg

Answered: -1 onto the line through 4 -3 and the…

Math

Advanced Math

-1 onto the line through 4 -3 and the origin. Compute the orthogonal projection of The orthogonal projection is

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Describe the product of two glide reflections whose axes are parallel.

A: The magnitude of the cross product of two parallel vectors was asked in this question. A glide…

Q: nd an equation of a plane passing through the following 3 points (1,-1,-1), (-4,1,4), (3,5,3)

A: topic- equation of plane through three points equation of plane passing through three points…

Q: A line passes through the point (9,1, – 1), and is parallel to the vector 7i + 3j + 7k. Find the…

A: We find the direction cosine first. As we know that the line is parallel to 7i+3j+7k So the…

Q: a/ the point (-2,-2√3) It is the Cartesian re ion of representation the polar vector (4, II) 3

A: Above question is solved.

Q: Which shows the image of the figure under a translation by the given vector? ADEF with vertices D =…

A: In this question we have to find which graph best describe the translation when vector is given.

Q: -(2) Find the equation for the set of all points whose distance from (-3,2,-1) is 4

A: our objective is to find the equation.

Q: A man starts at the origin and walks 8 meters East. He then turns and walks 8 meters North. Graph a…

Q: Starting with vector v in the diagram to the #9. right, graph the vector 3 v +w-2u Confirm your…

A: The graph is given

Q: The transformation Po[1, ₂] = cos²0 cos sin cos sin sin²0 [1, ₂] onto the line through the origin…

Q: (2x – 3y)dx – (-6y + 4x + 1 )dy = 0

A: Given that 2x-3ydx+4x-6y+1dy=0

Q: a) à = [ 7₁ -2], 6 = [2, -5] b) c = [ 3,5], j = [1, 2]

Q: Write the parametric equations of the line through the point (1,2,3) parallel to the vector a =.…

Q: What would be the new coordinates of A(2, 7), B(2, -3), C(5, 0) after a 90 degree clockwise…

Q: Apply the transformation -1 0 1=-1| For the vectors (1, 2) and (2,-3), perform the geometric…

Q: QUESTION 23 Find the vector equation of the line through the point 71and perpendicular to the plane…

A: The vector equation of a plane is, a→ is the vector on the plane given and r→ is the variable vector…

Q: Write matrix for 2D reflection about axes. Derive the transformation matrix responsible for the…

Q: Triangle ABC has points A(-1,2), B (0, -3) and C (1, 2). A translation of this triangle results in…

A: Observing from the given point we conclude that

Q: p1-2-is-the-image-of-p-after-a-translation-along-the-vector-8-0.-what-are-the-coordinates

Q: Which of the following describes 2D rotation? OxformMatrix.rotate(0, OxformMatrix.rotate(1,…

A: In two dimensions, the standard rotation matrix has the following form:

Q: Triangle CDE with vertices C(-1. 3). D(4,2). and E(3, 1): a) translated along the vector (-3. -7) b)…

Question

### Orthogonal Projection Problem

**Problem Statement:**
Compute the orthogonal projection of $\begin{bmatrix} -1 \\ 4 \end{bmatrix}$ onto the line through $\begin{bmatrix} -3 \\ 5 \end{bmatrix}$ and the origin.

**Solution:**

The orthogonal projection is $\begin{bmatrix} \boxed{} \\ \boxed{} \end{bmatrix}$.

Enter your answer in the edit fields and then click "Check Answer."

**Note:**
For computing the orthogonal projection of a vector $\mathbf{a}$ onto another vector $\mathbf{b}$, use the formula:

\[
\text{proj}_{\mathbf{b}} \mathbf{a} = \frac{\mathbf{a} \cdot \mathbf{b}}{\mathbf{b} \cdot \mathbf{b}} \mathbf{b}
\]

where $\mathbf{a} \cdot \mathbf{b}$ is the dot product of vectors $\mathbf{a}$ and $\mathbf{b}$.

### Instructions:
1. Calculate the dot product of the vectors.
2. Find the magnitude squared of vector $\mathbf{b}$.
3. Use the projection formula to find the result.
4. Fill in the boxes provided with the correct values.

**Diagram and Explanation:**
(In this case, there are no diagrams provided. An explanation of steps and formulae is included above.)

After computing, enter your answers and click "Check Answer" to verify.

### Example Calculation:
Given:
$\mathbf{a} = \begin{bmatrix} -1 \\ 4 \end{bmatrix}, \mathbf{b} = \begin{bmatrix} -3 \\ 5 \end{bmatrix}$

1. Compute the dot product $\mathbf{a} \cdot \mathbf{b}$:
\[
\mathbf{a} \cdot \mathbf{b} = (-1)(-3) + (4)(5) = 3 + 20 = 23
\]

2. Compute $\mathbf{b} \cdot \mathbf{b}$:
\[
\mathbf{b} \cdot \mathbf{b} = (-3)^2 + 5^2 = 9 + 25 = 34
\]

3. Use the projection

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Projection$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

the transfer of the coordinate system by the vector v = 21 +3j is carried out. The original coordinates of point P are (5, -2) and the new coordinates of point Q are (-4, 1). Determine the new coordinates of P and the original coordinates of Q
2. In a dance performance, four dancers form a diamond with vertices A(2, 0), B(0, 2), C(-2, 0), and D(0, – 2). Then, they move along the dance floor following the translation vector, (0, 4). There they pause, and then move again along the same vector. What are their coordinates after six such translations? а. А(26, 24), В'(24, 6), С'(22, 24), аnd D'(24, 22) b. A'(2, 10), B'(0, 12), C'(-2, 10), and D'(0, 8) c. A'(2, 24), B'(0, 26), C'(-2, 24), and D'(0, 22) d. A(26, 0), B' (24, 2), С'(2, 0), and D'(24, - 2) Name: ID: A
Find the maximum and minimum values of the function f(x, y) = 2x² + 3y² - 4x-5 on the domain 2 + y² 256. The maximum value of f(x,y) is: List the point(s) where the function attains its maximum as an ordered pair, such as (-6,3), or a list of ordered pairs if there is more than one point, such as (1,3), (-4,7). The minimum value of f(x, y) is: List points where the function attains its minimum as an ordered pair, such as (-6,3), or a list of ordered pairs if there is more than one point, such as (1,3), (-4,7).
Consider the points (1, 2,- 1) and (2, 0, 3). a. Find a vector equation of the line through these points in parametric form. b. Find the distance between this line and the point (1, 0, 1).
Solve this now in 20 min and take a thumb up
P(5,2,-1), Q(1,-3,-2), T(4,1,5) forms a triangle. find the vector projection of Rqp perpendicular on Rqt.