Let →a=⟨2,5⟩a→=⟨2,5⟩ and →b=⟨0,k⟩b→=⟨0,k⟩.Find k so that →aa→ and →bb→ will be orthogonal (form a 90 degree angle).

Q: Prove that the three points (;q, yx), (x2, y2), and (x3, y3) are collinear (lie on the same line) if…

A: Given : The three points are : x1, y1, x2, y2 and x3, y3 Now we have to prove that  x1, y1, x2, y2…

Q: Suppose that v1,..., Um is linearly independent in V and wE V. Prove that dim span(v1 + w,..., Vm +…

A: Let u1,u2,⋯,un be a set of vectors in a vector space V. This set of vectors is said to be linearly…

Q: Consider the vectors i = (2, – V3, 1) and ū = (-1, v3, 4). Find the orthogonal decomposition of u…

A:

Q: How do you know that for all a, b, c, d: ax + bx will be orthogonal to cx? + d ?

A:

Q: The vector projection of M = 2ax + 3ay + 2az onto P = 3ax + 2ay + 3az is

A:

Q: Suppose T E L(V, W) and v1, ..., Vm is a list of vectors in V such that Tv1,..., Tvm is a linearly…

A:

Q: (a) Prove that u + vand u - v are orthogonal in IR" if and only if ||u|| = ||v||. (b) Draw a diagram…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: If |r(t)| = c (a constant), then r' (t) is orthogonal to r(t) for all t.

A:

Q: A) compute x the component of x that is parallel to L and x the component of x that is orthogonal to…

A:

Q: The vector E %3D —а, — 4аф + За, еxpressed in RCS and in terms of ф is E 3 (-сosф + 4sinф)ax +…

A: This question is based on unit vector conversion from Cartesian to cylindrical system.

Q: find the distance d(u, v) between u and v in the given exercise.

A:

Q: Let u = (2,3, 1), v = (1,3,0), and w = (2,23, 3). Since (1\2)u – (2\3)v – (1\6)w = (0,0,0), can we…

A: No we can't

Q: { (0,0,0), (3,5,6)} is linearly dependent in R' ulgn O ihi O

A: A set containing the zero vector (0,0,0) is linearly dependent.  Therefore the given set {(0,0,0),…

Q: Prove that (i) the three points A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6) are collinear, (ii) the four…

A: (1) Given points are A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6)

Q: For all u and v in R" with u + 0, show that u is orthogonal to v – u•v

A:

Q: Find a relating ab and c Sothat the linear Systen X +2y- 2X +3 y +3Z = 6 5X +9y - 6Z = c eojarrar A…

A:

Q: UE Mn X, y E C" are If orthogonal if and only if Ux and Uy are orthogonal. is unitary show that

A: Given  is a unitary matrix, where Note a  matrix  is unitary if its conjugate transpose  is its…

Q: { (0,0,0), (3,5,6)} is linearly dependent in R ulgn O ihi O

A: Solve the following

Q: Let x = (1, 1, 1, 1)T and y = (8, 2, 2, 0)T . Verify that x − p is orthogonal to p.

A:

Q: Prove that if T:V-oW io a one to-one linear trans formation and 33 o a linearly deperdent then…

A:

Q: Find u × v and show that it is orthogonal to both u and v.u = (−2, 1, 1), v = (4, 2, 0)

A:

Q: Let v = (3, 0, 0) and w = (0, 1, −1). Determine u = v × w usingthe geometric properties of the cross…

A: Cross product: more formally called the vector product a way of multiplying two vectors and produces…

Q: Find u × v and show that it is orthogonal to both u and v.u = (1, −1, 1), v = (0, 1, 1)

A: Cross product is,

Q: Prove that if r(t) has constant length, then r(t) is orthogonal to r'(t).

A:

Q: Find the cross product ⃗a × b and then specifically verify that it is orthogonal to both ⃗a and b:…

A: Given data:     The first vector is: a=<a1, a2, a3>=<6, 0,-2> The second vector is:…

Q: 1. Let a = (1, 1, –1) and b = (2,4, 6). Find the cross product a x b and verify that it orthogonal…

A: Given: a=1, 1, -1b=2, 4, 6 To Find:  To find the cross product a×b, and, to verify that it is…

Q: {(0,0,0), (3,5,6) ) is linearly dependent in R ulgn O İhi O

A: Given {(0,0,0),(3,5,6)}

Q: Let Q be an orthogonalmatrix such that QA makes sense. Show that (QA)+ = A+QT.

A: The (Moore-Penrose) pseudoinverse of a matrix generalizes the notion of an inverse,somewhat like the…

Q: Let a = ci + jand b = 6i + 24j. Find c so that a and bare orthogonal. C =

A: Given : a=ci+jb=6i+24ja and b are othogonal   To Find : value of c

Q: 2. Show that the equations f(r, y,P. q) = 0 and g(r, Y.P. q) = 0 are compatible if %3D %3D a(f,g)…

A:

Q: Compute the orthogonal projection of i = onto the line L through and the origin. proj, (1) =

A:

Q: Let u = (1, 2, 3, 4), v = (0, 2, t, 3), and w = (1, 1, 0, 1). Find t so that u + v and w are…

A: Here, u=(1,2,3,4),v=(02,t,3) & w=(1,1,0,1)

Q: "Span(u1,..., in) = Span(71,..., Tn, w) if and only if J1,..., Un, w are linearly depen- dent."

A:

Q: The projection of v onto w is v=i+j+2k, and w=i+2j+2k 3 =(-i+j+2k) а. (i + 2j +2k) 5 -(i + 2j + 2k)…

A: Projection vector of a⇀ on the b→ is given by c→=a→·b→b→b^

Q: Use the Chain Rule to find ôz/əs and əz/ðt. z = tan(u/v), u = 4s + 7t, v = 7s – 4t Əz as az II

A:

Q: Suppose v,, v,,V3 are distinct points on one line in R" . The line need not pass through 29 the…

A:

Q: The projection of v onto w is v =i+j+2k, and w=i+2j+ 2k 3 (-i+j+2k) а. (i +2j+ 2k) (i + 2j+ 2k) 3 (i…

A:

Q: Let p = (2, t) and q = (3,5). Find t such that p and q are orthogonal. (Give your answer in two…

A: We will use the property of orthogonality

Q: 2. Show that the ry plane W = (r, y, 0) in R³ is generated by: (i)u = |2 and v= (ii)u = and v=

A: Please see the below picture for detailed solution.

Q: Find the cross product ax b. a - (1, 1, -1), b= (6, 8, 10) Verify that it is orthogonal to both a…

A:

Q: If So F.T ds = 0, then F and T are orthogonal. True O False

A:

Q: The vector E = = -a, – 4as + 3a, expressed in RCS and in terms of ø is Е 3 (-сosф + 4sinф)ax +…

A:

Q: Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w?

A: x is orthogonal to v and w. Then their dot product is zero. That is, ⇒x·v=0  &  x·w=0

Q: Show that the dyfferential equatian IS exact x(スt5in t) do + cast -2tu) abe +x² dt-

A: We will show that the given differential equation is exact.

Q: Find the orthogonal projection of v=2 onto W.

A:

Q: Let u = (2, 3, 1), v = (1, 3, 0), and w = (2, -3, 3). Since (1/2)u - (2/3)v - (1/6)w = (0, 0, 0),…

A: Given: u = (2, 3, 1), v = (1, 3, 0), and w = (2, -3, 3). And, (1/2)u - (2/3)v - (1/6)w = (0, 0, 0),…

Q: If v1, ..., V5 are in R' and v3 = 0, then {v, V2, V3, V4, V5} is linearly dependent. %3D

A: Definition used: v1, v2, ..., vk is linearly dependent if there exist numbers α1, α2, ..., αk, not…

Q: Let B= { }],19} be basis for IR. %3D Find [v]g where V= 15

A: Given :                          Basis  B = 3-30, 22-1, 114 and V = 15-93…