POWER SET & CARTESIAN PRODUCT. Let c= {2,3, 4, 5} B= {a, b, c, d} A = {0, 1} а. Ах ВxС b. СхВxА с. В х ВхВ d. Cx AxB

Q: Find u · v, u· u, ||v||2, (u · v)v, and u · (3v). u = (3, 11), v = (-4, 3) (a) u: V (b) u. u (c)…

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Q: What is the Cartesian product, if Let A = {x,y,z}, B={@,%}, C={0,1} A X B X C  C X B X A

A: Given A = {x,y,z} B = {@,%} C = {0,1}

Q: Let u = (5, - 3), v = (-2,9), and w = (0,- 2). Express 7u-3v+w in the form (a,b). %3D 7u -3v + w =…

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Q: u = (1,2, 0), v = (-1,4, 1)

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Q: Write each vector as a linear combination of the vectors in S (if possible).

A: Suppose that:    r= (1, 2,-2), s= (2,-1, 1) a) z=xr+ys z=x (1, 2,-2) +y (2,-1, 1) Hence,…

Q: If A={a,b,c,d,e,f} and B={k,l,m,n}, then find the Cartesian product ? × ? of A and B

A: Set of Each entry in 2 tuple in the below table is Cartesian product of A and B

Q: Part 3. Let U = {2,3,5, 7,11, 13, 17,19} A = {5,7,11, 13} B = {2} C = {13,17,19} D = {2,3,5} %3D…

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Q: Find u - v, 2(u + 3v), and 2v - u. u = (0, 3, 4, 4, 4), V3 (8, -3, -5, б, 3) (a) u - v = (b) 2(u +…

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Q: Find u · v, u· u, ||V|2, (u · v)v, and u · (3v). u = (3, -3, 5), v= (0, 6, 4) (a) u. v 2 (b) 43 u.u…

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Q: Naj bo A- (1,2,3, 4), B- (r. M.).C- (a,6). Dani sta funkciji : A + Bing:B-C - (1,). (2. y). (3, y).…

A: Given sets A=1,2,3,4, B=x,y,z & C=a,b. f is a function from A to B defined as,…

Q: Find u · v, u· u, ||v||2, (u · v)v, and u · (3v). u = (4, -3, 5), v = (0, 6, 4) (a) u: V (b) u.u (c)…

A: I am attaching image so that you understand each and every step.

Q: 2 Find Éu, 3v, v - u, and 2u + 5v. u = (7, 9), v = (6, -5) (a) -u (b) 3v (c) v - u

A: the given vectors are u=7,9 and v=6,-5.

Q: 2 Find u, 3v, v - u, and 2u + 5v. 3 u = (7, 6), v = (4, –4) %3D (a) u 3. (b) 3v (c) V - u

A: Given : u=<7,6> v=<4,-4>.

Q: 2. Find u, 3v, v-u, and 2u +5v. 3. u = (5, 3), v = (3, -2) %3D

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Q: Find u - v, 2(u + 3v), and 2v 8 u-(6,-8, 5, 3), v= (-2, 블,-을-1) (a) u - v = (b) 2(u + 3v) = (c) 2v –…

A: Given  u = (6,-8,5,3) v = (-2,83,-53,-1) (a)  u - v = 6 -(-2) , -8 -83  , 5 -(-53) , 3- (-1)  u -v =…

Q: Find u · v, v · v, ||u||², (u · v)v, and u · (5v). u = (2, 5, 0, –3), v = (0, 4, 4, 5) (a) u v (b)…

A: A. u.v So for u.v just multiply the element of u and v then add all multiplied value I.e.…

Q: If A = {1,2} and B = {3,4} then the Cartesian product A x B is A (3,4,6,8} B {(1,3), (1,4), (2,3),…

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Q: Find Jul, Iv], |2u], v, lu + vl, ļu – vl, and Ju| - |vl. u = 5i + j, v= 4i – 3j Jul = |v| = |2u| Ju…

A: Given: u=5i+j, v=4i-3j We know that if a= xi+yj+zk then a=x2+y2+z2

Q: Find u v, u·u, ||v||², (u · v)v, and u · (3v). (5, -2, 4), v = (0, 7, 5) U = (a) u V (b) (c) ||v||?…

A: The given vectors,  u=5,-2,4, v=0,7,5

Q: Find Jul, Iv], 12ul, v , lu + vl, lu – vl, and Ju| - Iv]. u = 3i + j, v= 4i – 2j Ju| = |v = |2u| =…

A: To find the following answers

Q: b= (-7,1) and č = (-4,–2). What is č +bin component form? Enter your answer by filing in the boxes.

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Q: Let u = (6, 3), v = (2, -9). Find 4u - 6 v.

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Q: Find u + v, 2v, u- v, and 3u - 2v. u = (1, -4, 2, 1), v = (0, 2, 2, 3) (a) u + v = (1, – 2,4,4) (b)…

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Q: Find u - v, 2(u + 3v), and 2v - u. u = (4, 0, -8, 6), v= (0, 2, 6, 4) (a) u - v - (b) 2(u + 3v) (c)…

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Q: 1) A curue with *a) = (2,4 4), 22)=(0,2,4). %3D Find K(2), B(2).

A: solution : Given α'→2=2,4,4α''→2=0,2,4find K2 & B→2=? formula of Kt=α't×α''tα't3now first we…

Q: Find u-v, 2(u + 3v), and 2v-u. u-(6, 0, -5, 8), v= (0, 4, 8, 6) u-v (b) 2(u + 3v) - (c) 2v-u-

A: To find out u-v, 2(u+3v), 2v-u

Q: roblem #15: Let -6 9. A = -6 -4 1 9. and let B = adj(4). Find b23, Le., find the entry in row 2,…

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Q: * vxu àu = (1,3,-3), v = (4,0,2) ......

A: Let's find.

Q: linear Combination write of vi,V2,V3 as Vz (2,7,10),V,=(1,2,3),V2=(1,3,5), V3 =(!,s,9) %3D

A: Consider the given values. V=2,7,10V1=1,2,3V2=1,3,5V3=1,5,9 Let's the linear combination of the…

Q: Find u, 3v, v – u, and 2u + 5u 3. u = (4, 3), v = (3, –3) 2. (a) 3

A: Given: u=4,3   v=3,-3

Q: (a) If A₁ = {-i, -(i − 1), . . .−3,−2,−1, 0, 1, 2 }, for i = 1, 2, 3,. . . find (i) Un A6 and (ii)…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Refer to B={ ={₁0, -6, 0.23, 3, -1.7, √7}. Determine which elements belong to the given set.…

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Q: Given v→ = and u→ = , find v→ + u→. v→ + u→ =

A: Given:     v  = ⟨ 10 , 2 ⟩      u = ⟨ -5 , 8 ⟩     v + u = ?

Q: Find u - v, 2(u + 3v), and 2v - u. u = (5, 0, -2, 6), v = (0, 9, 6, 5) (a) u - v =| (b) 2(u + 3v) =…

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Q: Find u - v, 2(u + 3v), and 2v – u. u = (5, 0, -3, 8), v = (0, 2, 8, 5) (a) u - v = (b) 2(u + 3v) =…

A: The objective of the question is evaluate the given values.

Q: u = ⟨−7, −1⟩, v = ⟨−4, −1⟩, find (a) u ∙ v, (b) u ∙ u, (c) || v ||2 , (d) (u ∙ v)v, and      (e) u ∙…

A: Hey, since there are multiple subparts are posted, we will answer first three subparts.

Q: U = {a, b, c, d, .., n} A = {a,b, e, ƒ, i, j, m, n} • B= {a, b, d, g, k} %3D %3D C = {b, d, f, h, j,…

A: To Construct a Venn diagram illustrating the following sets:

Q: Find u - v, 2(u + 3v), and 2v - u. и%3D (6, —8, 5, 3), v = (-2, - -1) (a) u - v = (b) 2(u + 3v) =…

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Q: u = ⟨3, 4⟩, v = ⟨−1, 5⟩ Find         (a) u ∙ v, (b) u ∙ u, (c) ||v ||2 , (d) (u ∙ v)v, and      (e)…

A: Given vectors are u=3,4 and v=-1,5. Given vectors can be written as: u=3i+4j and v=-i+5j. (a)…

Q: AB¯¯¯¯¯¯¯¯AB¯ has endpoints at A(2,6)A(2,6) and B(6,8).

A: GIVEN: A (2, 6) = (x1 , y1) and              B (6, 8) = (x2, y2) TO FIND: equation of the line

Q: given u = and v= find 2u+5v

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Q: Find u, 3v, v-u, and 2u + 5v. u (5, 3), v (4,-5) (a) u (b) 3v (c) v-u (d) 2u + 5v

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Q: If v = i - 2j + 2k, u= 4i - 3k the Projuv is : 6. i + 25 -8 -1 -i + 25 25 25 Option 3 O Option 1

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Q: Find u - v, 2(u + 3v), and 2v – u. u = (3, 0, 4, 4, 4), v = (6, 3, -3, 8, -5) (a) (b) 2(u + 3v) =…

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Q: Find u · v, u· u, ||v||2, (u · v)v, and u · (3v). u = (5, -2, 4), v (0, 7, 4) (a) u: V (b) (c)…

A: Dot product of two vectors u=<a,b,c>,v=<x,y,z> is defined by, u.v=ax+by+cz Norm of a…

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.