u→=⟨−5,−3,−5⟩ and v→=⟨−4,−2,−1⟩.

Q: Calculate F. dĩ, where C is the square of (1,1, 1), (–1, 1, 1), (–1, –1,1) and (1, –1,1), with…

A:

Q: One of the following vectors lies in span{ 2+x + x?, 3+x- 2x2} (A) 4+ x – 7r² (B) 4+ x – 4x? (C) 4 +…

A: Solve the following

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: The diagram approximately Illustrates how the planes intersect. x+y+z+1=0 2x+2y+2z+1= 0 3x+3y+3z+1=0…

A: Given planes are,    x + y + z + 1 = 0  2x + 2y + 2z + 1 = 0  3x + 3y + 3z + 1 = 0    Thus, normals…

Q: What should k be if the vectors x=(1,1,k) y=(1,3,1) z=(k,1,3) are in the same plane in the Euclidean…

A: Three vector a1,a2,a3,b1,b2,b3 and c1,c2,c3 will be in euclidean space ℝ3 If  a1a2a3b1b2b3c1c2c3=0…

Q: 2. Given A = {1,2,3}, B = {7,apple, .5} and C = {r|x < 3 and r 2 -1}, compute the following %3D %3D…

A:

Q: If W(-10, 4), X(-3, -1), and Y(-5, 11) dassify AWXY by its sides. Show all work to justify your…

A: Given,           If W-10, 4, X-3, -1, and Y-5, 11 of ∆WXY.

Q: The projection of onto the line through zero and is a. (G) b. d. 0.

A:

Q: Find the length and direction (when defined) of u x v and vxu. u= 5i + 3j – 5k, v=0

A: we know that  uxv=|u|.|v|sin∅.n^where ∅ is angle between u and v and n^ is unit vector perpendicular…

Q: 3. Sketch the points determined by the following. (a) Iz+1-i = 2 %3D (b) Im(2z +i) +1=0

A:

Q: Let ūi= 3. 5 %3D and u = Uz %3D Is V= 田。 e Span

A:

Q: Discussion: 1- Show that Ramp(t) = u(t) dr = t * u(t)

A: The ramp function is very significant function in mathematics. It is the composition of two…

Q: The orthogonal projection of v = 10i on b = −3i + j is _____ .

A: To find the orthogonal projection of v = 10i on b = −3i + j .

Q: Find the length and direction (when defined) of u x v and vxu. u= - 12i + 9j – 12k, v = - 4i + 3j –…

A: Using formula of u x v and v x u,

Q: (G) G)- The projection of onto the line through zero 1 is and а. (;) () " () b. C. d.

A: Let u→=11, and the line l through zero v→=00, and w→=1-1. Need to find the projection of u→ onto the…

Q: In Exercises 1–8, find the length and direction (when defined) of u X v and v X u. 1. u = 2i – 2j –…

A:

Q: graph the points z = x + iy that satisfy the givenconditions.a. | z | = 2 b. | z | &lt; 2 c. | z |…

A: a. We have given z=2 Then, put z=x+iy This implies that x+iy=2x2+y2=2x2+y2=4 Therefore, x2+y2=4…

Q: Suppose that a linear transförmation / satisfies T(u,) = T(u,) = -1 -2 Find T(4u, - 3u,). T(4u, -…

A:

Q: 4. Evaluate . F.ds , where C is the triangle with vertices (1,0,0), (0,2,0), and (0,0,3) oriented by…

A:

Q: Write the projection of 2î +3j-k along the vector î+j.

A: Given that: 2i+3j-k along the vector i+j.

Q: Which of the following would be a line of reflection that would map ABCD onto itself? 3 B 2 D Ox=1…

A: For the solution follow the next steps.

Q: The transformation (x, y)(-x, y) reflects the preimage across the diagonal line y = x. O True O…

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=&lt;a1, a2, a3&gt;=&lt;6, 0,-2&gt; The second vector is:…

Q: The notation (x, y) → (-x, y) defines a reflection on the coordinate plane, O True O False

A: Solving the problem by helping of a point.

Q: Let x,y ∈ Rn Show that: |x + y| 2 + |x - y|2 = 2|x|2 + 2|y|2

A:

Q: If the plane F contains the points P(1, 0, 0), Q(3, 2, 0), R(0, 2, 1), L O 1 6 -6 O -2

A:

Q: Find the orthogonal projection of y onto u. y = -3/5] - 4/5 /5 4/5 b) c) d) 2.

A: The formula to find the orthogonal projection of y onto u is: projuy=u→.y→u→2.u→ Here,…

Q: Find the orthogonal projection of y onto u. - 8 4 y = u: 6. 12 O A. 1 4 3 4 О В. 4 12 Ос. 16 48 O D.…

A: We have to find orthogonal projection of y on u.

Q: Verify that it is orthogonal to both a and b. (a × b) · a = (a × b) · b = %3D

A: Given

Q: Calculate , (7xy+ 3e²) dS, where S is the triangle with vertices (0,0, 3), (1,0, 2), and (0, 4, 1).…

A: Given vertices of triangle are 0,0,3 ,1,0,2 ,0,4,1 Let the equation of plane through these points…

Q: The diagram approximately illustrates how the planes intersect. x+y+z+1=0 2x+2y+2z+1=0 3x+3y+3z+1=0…

A: True

Q: z= 2e'+i

A:

Q: Find the cross product axb. 1+9k, b- 41-j+ 3k Verify that it is orthogonal to both a and b (a xb) (a…

A:

Q: 8) Find the cross product a x b and verify that it is orthogonal to both a and b. a = (1, 1, -1),…

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Q: Calculate the projection of f = 4 i - j +7k on g = 3 i +2j – 6 k

A: Projection in vector:       The vector projection of a vector a on (or onto) a nonzero vector b…

Q: In the xy plane mark all nine of these linear combinations: c[2/1]+d[0/1] with c=0, 1 , 2 and d=0, 1…

A:

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: Find the length and direction (when defined) of u xv and vxu. u= - 12i + 8j – 20k, v = - 3i + 2j -…

A: To find the length and direction of u→×v→, first find the value of u→×v→ by cross product. The given…

Q: r = (6,-3,2)+1(2,0,1) + u(1,1,–3)

A: Given point is (0,-1,-8) and the plane is r→=6,-3,2+t2,0,1+u1,1-3

Q: Find the projection of a on the plane P if a 4 and P has the equation x + y + z = 1.

A:

Q: If u = (3, −1, 4) and v = (−2, 3, 5), the scalar projection of y onto v is:

A:

Q: 4. let f(x, y) = x² – xy + y² – y. find the direction u and Duf at Po(1,–1) for which Duf is the…

A: Given:- f(x, y) = x2 -xy+y2 -y To find:- Direction u and Du f at point p0 (1, -1) for which Du f is…

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: The orthogonal projection of v = 10i on b = –3i + j is <

A:

Q: Consider AB in the coordinate plane below. 10 7 5 4 3. 2 A B 6 7 89 10 10-9 -8 -7 -6 -5 -4 -3 -2 -1…

A: i am going to solve the given problem by using some simple geometry to get the required result.

Q: 1. Let T: R3 R3 be a linear image, which satisfies that (-3 Tei = -3/22, T(ez) = 9/2 and T (es) = -3…

A:

Q: Find the coordinates of the reflection across y=-1 A) R(1, 0), Q(5. –1), s(3, 4) C) R(0, -1), Q(-1,…

A: Co ordinate Geometry question

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…