Refer to the vectors u, to ug. -5 1 1, u2 = u3 = U4 = -5 U5 4 4 Compute projs u8, where s = span{u5, u7}.

Q: Find the vector v with the given length and the same direction as u.||v|| = 4, u = (−1, 1)

A: To find a vector v with the given magnitude of ||v|| = 4 and in the same direction as u = (−1, 1).

Q: Find the distance between the two vectors: u = (-5, 6, -5), v = (-3, 4, 5) Select one: O A. 2/41 O…

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Q: For the vectors u= (-3,0,4) and v= (1,3, - 3), calculate projyu and scal, u. proj, u = OOD

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Q: Find the unit vector having the same direction as v. v = 3i + - 4j O A. u= 15i + - 20j OB. u- - 5 B.…

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Q: Determine if i = (1,0.-4) and w=(9,3,1) are parallel vectors.

A: Use the vector product to show the given vectors are parallel.

Q: 3 Give the position vectors of A, B, C, D and E relative to O for the diagram below. B D-

A: In geometry a position vector so known as location vector. Here we find position vector relative to…

Q: Suppose that uj and u2 are orthogonal vectors, with u1 = 2 and u2|| = 4. Find |5u1 - u2 ||. ||5u1 -…

A: We have to solve given problem: Let  U1=(a1,a2)  U2=(b1,b2)5U1-U2=5(a1,a2)-(b1,b2)…

Q: Find the vector component of v = (4, – 1, 7) alongb = (1, 2, –2) and the vector component of v…

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Q: Given the vectors u=(2,1,1,1) and v=(3,2,-1,2) ,find the value(s) of such that  U•(u+tv)=16

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Q: Let i = [-1 4] and j = [-4 1]. Find the following vectors. i = 62 i = -6j = | w = 62 – 6ỹ = = [ -

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Q: For the vectors u=−1,4 and v=−4,2​, calculate projvu and scalvu.

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Q: .b,č are three vectors such that a + b+ e = 0, lal = 5.6 = 3. = 8 then ä.b+ ans. -49 48 1/6

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Q: Find the angle 0 between vectors u = 2i - jand v = 6i + 4j.

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Q: and = Wnte Pas the sum of two orthogonal vectors, 2 in S panƐu} and orthogonal to .

A: Given that y→=51 and u→=36.It is required to write y→ as the sum of two orthogonal vectors, x1→ in…

Q: If u =(3, 3), v=( 13. -7), and 2w +3u-v= (4,-4) then what is the coordinate of vector w?

A: Since u=(3,3), we have u→=3i→+3j→ Also, since v=(13,-7), we have v→=13i→-7j→ Let w=xi→+yj→ Given…

Q: Find the distance between the two vectors. u = (24, 14, 19), v = (-4,4,7) Select one: O A. 50 OB.…

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Q: For the vectors u= ,0,2) and v= ,- 3), calculate projyu and scal, u. projy u = O DD

A: Given ,the vectors u=-4,0,2  and   v=1,3,-3

Q: Find vector c = 3u – v, if u = and v =.

A: Given u = 2i - 7j + 3k and             v = 0i + 4j -  k = 4j - k Now vector c = 3u - (1/2)v c = 3(2i…

Q: u * v =( u1v1, UzV2 , Uz V3 , · Un Vn).

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Q: Determine R21, the vector from P2(5, 2,–4) to P1 (3, –1,0). 2аx + Зау — 4а, — 2ах — Зау + 4a, | 4ах…

A: Given the points P25,2,-4 and P13,-1,0. To find vector R21 from above two points. The vector from…

Q: * For the vectors v=16,8) and W=18,6), validate the Schwarz and Triangle mequaiity and fino the…

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Q: Find the components of the vector ī, with |u| = 7.8 and 0 = 21.3°.

A: Given: To Find:  The components of given vector  Formula Used: The components of vector v with…

Q: Find the unit vector having the same direction as v = (1, - 3). %3D 1 3. V 10 V10 10 V10, 3. O (1,…

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Q: Determine whether or not the given two vectors are parallel.u =〈4, 2, -6〉, v =〈2, -1, 3〉

A: To determine whether or not the given two vectors are parallel.u=4,2,-6 and v=2,-1,3 By definition,…

Q: Which vector below is NOT orthogonal to i = -2î – 8ŷ + 7k ? -- 1 2 8. O 0 î + 0ĵ + 0k 3. 1 O 4 î - )…

A: Given problem:-

Q: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

Q: 1 -E---Fl 2 V2 = 0 , and v3 = -5 span R³? Why or why not? 3 Do the vectors V₁ = -31

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Q: Find the vector V with the given magnitude and in the same direction as " M-;; -( 5 u = 4 - 6, 8)

A: We have to find vector

Q: Use the vectors u = (6, 6) and v = (-9, 3) to find the indicated quantity. (u - v)v (u · v)v =

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Q: Use the vectors u = (4, 4), v = (-7, 2), and w = (4, –1) to find the indicated quantity. (u · v) –…

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Q: For each pair of vectors, calculate projvu and the vector component of u orthogonal to v. (a) u =…

A: Vector components

Q: Find the vector w which is of length 6 and oppositely directed to u=(2,-2,1) Select one: O None W=…

A: A vector oppositely directed to  u⇀ = <2,-2,1>  is  w = − u = − <2,-2,1>  i.e.  w =…

Q: For the vectors u = (- 3,5) and v = (- 5,2), calculate proj,u and scal,u.

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Q: Find a unit vector in the direction of u = (5, 3, 2).

A: Given vector is u=(5,3,2) Find a unit vector

Q: If U1 and U2 are orthogonal unit vectors and V = aU1 +b U2, find V.U.

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Q: 1) Check whether the vectors 효-1 33 5], -[3 10 6 T T Va = [2 7 3 2]' are line orly independent.

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Q: 27-j+4k sī +2j-2k.

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Q: Consider the vectors u = (7,1,5, -5) and i = (3,4, c, 0) in R*. a. Find the value of c that will…

A: Given, The unit vector is in the same direction as u→=7,1,5,-5.

Q: If u = 2i -j- 3k, w = 3i – 9j+ 5k and v = perpendicular. 15i – 3j – 5k, then the vectors are Select…

A: which option?

Q: 2. (a) Compute ||(1,2, 3)||- (b) Find the angle between the vectors (1, v3) and (1,0).

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Q: Find the vector projy 2i - 2j - 4k, u = 5i - 12 k

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Q: Repeat the directions of Exercise 3 with the same vector w, but with u, = uz = -2 u = u u = |-3 9-…

A: Please find the answer in next step

Q: 4 3 Which weights should be used for b = a, vị + a2 V2 to obtain the vector b = ? 2 a1 = Ex: 42 az =

A: Solve the following

Q: Find the angel between the vectors u and v if u=-4i+2j and v=3i+2j Round answer to two decimal…

A: Consider the dot product of two vectors.

Q: 20. Show that the pair of vectors ' and ¯J is perpendicular.

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Q: Determine if the vectors t= %3D(-16, 24) and s= (3, 2). are orthogonal, parallel, or neither.

A: We have to calculate dot product and magnitude of the given vectors

Q: value

A: If, P, Q & R are collinear, then,  The position vector of QP is, The position vector of P - the…

Q: Find a unit vector u in the direction opposite of v = (2,8,-3).

A: Solution ) v =  { 2 , 8 , -3 }   vector with same magnitude and opposite direction   = { -2 , -8 , 3…

Q: Use the points P(3, 1) and Q(7, 1) to find position vectors equal to PQ and QP.

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Q: Find the distance between the two vectors. u = (4, – 8), v = (- 8,8) O A. 100 О В. 4 Ос. 20 O D. 400

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.