Question: Let W be the line with parametric equations x = 2t, y = - t, z = 4t (- < t < ) (a)

Let W be the line with parametric equations
x = 2t, y = - t, z = 4t (- ∞ < t < ∞)
(a) Find a basis for W.
(b) Use Formula 6 to find the standard matrix for the orthogonal projection onto W.
(c) Use the matrix obtained in (b) to find the orthogonal projection of a point P0(x0,y0,z0- zo) onto W
(d) Find the distance between the point P0(2, 1,-3) and the line W.

Step by Step Solution

★★★★★

3.34 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The vector v 2 1 4 forms a basis for the line W b If we let A v T then th... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

938-M-L-A-E (1329).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Find the vector form of the equation of the line in IR3 that passes through P = (- 1, 0, 3) and is parallel to the line with parametric equations x = 1 - t y = 2 + 3t z = - 2 - t

Find the distance from the point (3, 2, 5) to the line with parametric equations x = t, y = 1 + t, z = 2 + t.

Find the vector and parametric equations of the following lines. (a) The line passing through P(3, -1, 4) and Q(1, 0, -1). (b) The line parallel to [1 1 1]T and passing through P(1, 1, 1). (c) The...

Part A: Knowledge (16 marks) 1. Let L, be the line with vector equation r = (-2,3) + s(-1,3), s E R. Let L2 be the line with parametric equations x = 3t + 2, y = t - 7, t E R. Are the two lines...

PART A: KNOWLEDGE AND UNDERSTANDING Multiple Choice. Place the appropriate answer in the space provided. 1 mark each. i . Which of the following is a direction vector for the line with Cartesian...

Please help me with this, I'm stuck Let L be the line with parametric equations x = -8-3t y =7-3t z=-8+2t Find the vector equation for a line that passes through the point P=(-9, -9, 2) and...

Can you help me answer number 23? A line has para equations x= -2t+2 and y=4t+6. What is the slope of the line representing y in terms of x? A. 4 B. 2 C. -2 D. -4 E. None of the Above 23. (L62) A...

A simple question from mathematics, send me the final answer quickly, please Let P(, y, z) be the point at which the line with parametric equations x = 2-t, y = 3 +2t, z=1-t, teR, 2x - y + z= -3....

Find the point at which the line with parametric equations x = 2 + 3t y = 4t, z = 5 + t intersects the plane 4x + 5y 2z = 18.

Let L be the line with parametric equations x = 4-1? 3/ = -8+2t z = -5+2t Find the vector equation for a line that passes through the point P=(3, 5, 5) and intersects L at a point that is distance 4...

Reread the Management Focus feature on U.S. Magnesium Seeks Protection (chapter 7). Who gains most from the anti-dumping duties levied by the United States on imports of magnesium from China and...

The random variable X can take on only the values 0, ±1, ±2, and (a) Find the probability distribution of X. (b) Graph the CDF of X. (c) Compute E(X). Pi-l

In Java, multidimensional arrays are: q , A special type of array that requires a library to use. None Only possible to create with dimensions of 2 2 or greater. Arrays of arrays, where each element...

16. Suppose the Korean government implements policies that modernize plant and equipment, promote innovation, and enhance labor productivity. As a result, the nations aggregate supply rises without...

det(A + B) = det(A) + det(B) In the case of a true statement, explain or prove your answer. In the case of a false statement, give an example to show that the statement is not always true. In each of...

det(A) = det(B) implies A = B. In the case of a true statement, explain or prove your answer. In the case of a false statement, give an example to show that the statement is not always true. In each...

det(Ak) = det(A)k In the case of a true statement, explain or prove your answer. In the case of a false statement, give an example to show that the statement is not always true. In each of the...

Modern Artifacts can produce keepsakes that will be sold for $60 each. Nondepreciation fixed costs are $3,000 per year and variable costs are $30 per unit. a. If the project requires an initial...

Williams software has 7.9% coupon bonds on the market with 22 years to maturity. The bonds make semi annual payments and currently sell for 109% of par. A. What is the current yield on the bonds? B....

The IRS provides a toll-free helpline for taxpayers to call in and get answers to questions as they prepare their tax returns. In recent years, the IRS has been inundated with tax payer calls and has...