(3) Let L be the line yplane, the product CD2r in the plane. Find a matrix C such what for every vectoronto the line L.is equal to the orthogonal projection ofin the

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Answered: (3) Let L be the line y 2r in the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let I be the line in R³ that consists of all scalar multiples of the vector w = Find the reflection of the vector v = (81 reflection = 2 -[1] 2 [8] 8 in the line L.
3. Determine all three dimensional vectors that are orthogonal to v = 5î – 5ĵ – 5k
6. Project the vector b = (1, 4, 2) onto the plane S that contains the vectors a₁ = (1, 2, 1) and a2 = (1, 1,0). (i) Find the 3 x 3 projection matrix P onto S. (ii) Show that P2 = P. (iii) Find a vector whose projection onto S is the zero vector. (iv) Show that I - P projects onto the line perpendicular to S.
5. Find the orthogonal projection of the vector b = vectors V₁ = -1- and v2 = onto the subpace E spanned by the (Note that v₁ V₂).
If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from a point P to the line L is equal to the length of the component of the vector AP that is orthogonal to the vector AB. P A B Use the method above to find the distance from the point P(-3, 1, 11) to the line through A(1, 1,0) and B(-2,3, –4). NOTE: Enter the exact answer. Distance
Let a = (-6, 2, 7) and b = (10, –1,6) be vectors. (A) Find the scalar projection of b onto a. Scalar Projection: (B) Decompose the vector b into a component parallel to a and a component orthogonal to a. Parallel component: ( Orthogonal Component: (
If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from a point P to the line L is equal to the length of the component of the vector AP that is orthogonal to the vector AB. P L B Use the method above to find the distance from the point P(-3,1, 12) to the line through A(1,1,0) and B(-2,3, –4). NOTE: Enter the exact answer. Distance = %3D
If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from a point P to the line L is equal to the length of the component of the vector AP that is orthogonal to the vector AB. L A Use the method above to find the distance from the point P(-3, 1,5) to the line through A(1,1,0) and B(-2,3, –4). NOTE: Enter the exact answer. Distance
Compute the curl of each of the following vectors: V = (yz, xz, xy) F = (x, y, z) = = ( Note: Y 2 (x² + y² +2²)³/²¹ (x² + y² + x2)³/²¹ (x² + y² + x2)³/2 • If the answer is a scalar, you can just type it in the box (using the Calcpad if you like, or using / for fractions, ^ for exponents, etc.) For multiplication, you can either leave a space, or use *. So x*x=xx = x². Note that this is not the same as xx without a space; that will get read as an entirely different variable! • If you need to enter a vector, enter an ordered list of components, so for A you can enter either A = (A₂, Ay, A₂) = {Ax, Ay, Az} . Note that the system isn't great with multiplying through by overall factors, so it's better not to write e.g. • If you need to enter O, enter it in three components, as (0, 0, 0) or {0,0,0}. V x V = ▼ xr= vx= (2A, 2A, 2A₂).

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(3) Let L be the line y 2r in the plane. Find a matrix C such hat for every vector H plane, the product C U is equal to the orthogonal projection of H onto the line L. in the