1. Let Q = (-3.-3.-3.3), R = (-3.-3,-33) and S = (1,10,10.1). In the following, when...

Question

Question

1. Let Q = (-3.-3.-3.3), R = (-3.-3,-33) and S = (1,10,10.1). In the following, when rounding numbers, round to 4 decimal pla

Answer 1

Answer #1

1 O Led Q = (-3, -3, -3.3) R= (-3,-3, -33) S=(4, 10, 10.1) QR = RS (11) Let o be the angle belveen De and R-Q = (-3, -3, -33)

Answer 2

Similar Homework Help Questions

1. Let Q = (-3, -3, -3.3), R = (-3, -3, -33) and S = (1,...

1. Let Q = (-3, -3, -3.3), R = (-3, -3, -33) and S = (1, 10, 10.1). In the following, when rounding numbers, round to 4 decimal places. (i) Find QŘ and RS. (ii) Find ||QR|| and ||RŠI. (iii) Find the angle in degrees between QR and RS. (iv) Find the projection of RŠ onto QŘ. 2. Let v= [6, 1, 2], w = [5,0,3], and P = (9, -7,31). (i) Find a vector u orthogonal to both v...
2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find...

2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w. (ii) Let L be the line in R3 that passes through the point P and is perpendicular to both of the vectors v and w. Find an equation for the line L in vector form. (iii) Find parametric equations for the line L.
3. Consider the following system of linear equations: 2x + 2y + 2kz = 2 kx...

3. Consider the following system of linear equations: 2x + 2y + 2kz = 2 kx + ky+z=1 2x + 3y + 7z = 4 (i) Turn the system into row echelon form. (ii) Determine which values of k give (i) a unique solution (ii) infinitely many solutions and (iii) no solutions. Show your working. 2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w....

(3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A- (3 points) Let W be the subspace of R spanned by the vectors 1and 5 F...

(3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A- (3 points) Let W be the subspace of R spanned by the vectors 1and 5 Find the matrix A of the orthogonal projection onto W A-
Will rate once all is completed. 1) 2) 3) 4) (12 points) Find a basis of...

Will rate once all is completed. 1) 2) 3) 4) (12 points) Find a basis of the subspace of R that consists of all vectors perpendicular to both El- 1 1 0 and 7 Basis: , then you would enter [1,2,3],[1,1,1] into the answer To enter a basis into WeBWork, place the entries. each vector inside of brackets, and enter a list these vectors, separated by commas. For instance if vour basis is 31 2 and u (12 points) Let...
Problem 13. Let l be the line in R' spanned by the vector u = 3...

Problem 13. Let l be the line in R' spanned by the vector u = 3 and let P:R -R be the projection onto line l. We have seen that projection onto a line is a linear transformation (also see page 218 example 3.59). a). Find the standard matrix representation of P by finding the images of the standard basis vectors e, e, and e, under the transformation P. b). Find the standard matrix representation of P by the second...

Q6. Let W be the subspace of R' spanned by the vectors u. = 3(1, -1,1,1),...

Q6. Let W be the subspace of R' spanned by the vectors u. = 3(1, -1,1,1), uz = 5(–1,1,1,1). (a) Check that {uj,uz) is an orthonormal set using the dot product on R. (Hence it forms an orthonormal basis for W.) (b) Let w = (-1,1,5,5) EW. Using the formula in the box above, express was a linear combination of u and u. (c) Let v = (-1,1,3,5) = R'. Find the orthogonal projection of v onto W.
Problem l: Let u, v and w be three vectors in R3 (a) Prove that wlv +lvlw bisects the angle betwe...

Problem l: Let u, v and w be three vectors in R3 (a) Prove that wlv +lvlw bisects the angle between v and w. (b) Consider the projection proj, w of w onto v, and then project this projection on u to get proju (proj, w). Is this necessarily equal to the projection proj, w of w on u? Prove or give a counterexample. (c) Find the volume of the parallelepiped with edges formed by u-(2,5,c), v (1,1,1) and w...
(12 points) Let vi = 1 and let W be the subspace of R* spanned by...

(12 points) Let vi = 1 and let W be the subspace of R* spanned by V, and v. (a) Convert (V. 2) into an ohonormal basis of W NOTE: If your answer involves square roots, leave them unevaluated. Basis = { (b) Find the projection of b = onto W (c) Find two linearly independent vectors in R* perpendicular to W. Vectors = 1

All vectors and subspaces are in R”. Mark each statement True or False. Justify each answer....

All vectors and subspaces are in R”. Mark each statement True or False. Justify each answer. Complete parts (a) through (e) below. a. If W is a subspace of R" and if y is in both W and wt, then y must be the zero vector. If v is in W, then projwv = Since the wt component of v is equal to v the w+ component of v must be A similar argument can be formed for the W...