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

Q: If a vector u is orthogonal to vectorsx and y then u is orthogonal to the vector x + y.

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Q: Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope of the…

A: Given: Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope…

Q: onow that the v ectors 2 3 do not span R' by giving a vector not in their span.

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Q: Find the angle 0 between the vectors. u = (2, 2), v = (4, -4)

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Q: Assume that the vectors u = ai-j+k and w=i+9j+5k orthogonal. Then the are value of a is

A: If two vectors are orthogonal (perpendicular), then their dot product is 0. We use this to solve the…

Q: Let f(x, y) = 5y² In(4x). Then Duf(1,4) in the direction of the vector (-2,-2) is

A: The explanation of answer as follows

Q: Suppose that u and v are vectors in R7 both of length 2/2 and that the length of u- vis also2 /2.…

A: We can evaluate  the given problem as follows:

Q: Consider two vectors A and B prove that the cross product between them can be calculated as follows…

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Q: 8. Let C = 2 c=(; 1) - (;) ()- and b = Find a 2-vector z such that Cz = b.

A: we have  C=112-1b=11   we have to find a 2-vector such that  Cz=b

Q: u.v<0, u.w < 0 ,w .u < 0 ?

A: Given data:     The given first vector is: u. The given second vector is: v. The given third vector…

Q: Consider two vectors A and B prove that the cross product between them can be calculated as follows…

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Q: In general, show that the vectors V = ai + bj and W = -bi +aj are always perpen-dicular. Assume a…

A: Given vectors are v=ai+bj and w=-bi+aj, where a≠0 ,b≠0. We know that two vectors are perpendicular…

Q: 1. Compute the following for the vectors in R3, x [1 3 21T and y [40 1T y and y x (a) (b) 2 and y2…

A: From the given information, [1 3 –2]T and [4 0 –1]T.

Q: Q2/ Show that the vector v = ai + bj is perpendicular to the line ах + by + с.

A: A line and the vector  are said to be perpendicular to each other when the product of their sloped…

Q: 2 Find the angle between two vectors Ā - Hax-Gay -89z B-Gax + 10ay + Saz

A: Angle between two vectors A⇀ and B⇀ is θ=cos-1A⇀·B⇀A⇀B⇀

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

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Q: 1. Show that the necessary and sufficient condition for two nonzero vectors A and B to be…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: Find a non-zero vector x perpendicular to the vectors 3 13 and u =| 4 -4 3

A: Let's find.

Q: What three points are on the line L: vector r= (2,-5) + s(2,1), sER

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Q: Represent the line segment from P to Q by a vector-valued function. P(7, 0, 9), Q(6, −6, 7) r(t)…

A: Given: Represent the line segment from P to Q by a vector-valued function. P(7, 0, 9), Q(6, −6, 7)…

Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Let x3 = x1 + x2. Determine the length of…

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Q: Suppose that u and v are vectors in R7 both of length 2 /2 and that the length of u - v is also2 /2.…

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Q: Show that the vector v = ai + bj is perpendicular to the line

A: GivenVector V = ai + bj and the line ax + by + c

Q: 42. Show that the unit vector ī = xỉ + yj is not parallel to ū = yi – xj for any choice of x and y.

A:

Q: Q2/ Show that the vector v = ai + bj is perpendicular to the line ax + by + c.

A: Condition for perpendicular is: m1m2=-1 Part A: Consider the vector v=ai+bj x component of vector =…

Q: 9. Which is traveling faster, a car whose velocity vector is 217 +35j or a car whose velocity vector…

A: We are authorised to solve only one question, please repost remaining questions Magnitude of vector

Q: Show that ū = aitbj is perpendicular to the line ax+by=C by establishing that the slope of the…

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Q: State the Cauchy-Schwarz Inequality and use it for solving the two vectors in R3 if x = [1,-2,4] and…

A: Cauchy schwarz inequality -  For any vectors u and v in an inner product space V,  |&lt;u,v&gt;|…

Q: Show that the vector ñ = 2î – 3j is perpendicular (orthogonal) to the line 2x – 3y – 6 = 0.

A: to Show that the  given vector is perpendicular to the  given line

Q: Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in the figure below,…

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Q: Realize the Cauchy-Schwarz inequality for the vectors x= ( -1, 2, 4,3), y=(0,-2,1, 4) ∈ R4 and find…

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

Q: State the difference between a position veetor and a line vector.

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Q: 9. Show that for any real numbers a and b the vectors u = ai and v = bj are orthogonal?

A: Topic:-  vector algebra

Q: Consider two vectors A and B prove that the cross product between them can be calculated as follows…

A:

Q: 1. Plot the following vectors using arrows on an xy-graph: -- (}). v-[+]. 1 u = V = 2u, u+v. Is…

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Q: Is it always true that T(0) = 0 where the zero vectors live in the appropriate spaces? Justify

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Q: 2. Can three vectors in the xy plane R2, have u v < 0, v w < 0, w u<0?

A: Given that, u, v and w are vectors in XY plane. The dot product of vectors is defined as, if u = a1…

Q: State the condition that the two vectors i and y are perpendicular. Find the value(s) of k such that…

A: If two vectors are perpendicular to each other, then their dot product is equal to zero.

Q: State the Cauchy-Schwarz Inequality and use it for solving the two vectors in R³ if = [1,–2,4] and y…

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Q: Let f(x, y) = 5y² ln(4x). Then Duf(1,4) in the direction of the vector (-2, –2) is

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Q: What value(s) of a are necessary for vectors i = (2, a), and w = (4a, 3) to span R?

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Q: 2. Find a vector that has the same direction as (-3, 5, v2), but has length 8. 3. If ā = 21 – 43+ 4k…

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

Q: 12. Suppose that ú = (a, b) is a non-zero vector in R², where a ± 0. Show that the line L =…

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Q: What is the dependence on the following vectors: u=(3.0.1), v=(1,-1,0) and w=(1.0.1) thanks!

A: A set of vectors {v1,v2,...,vn} in Rn is said to be linearlyindependent if the vector equationx1v1 +…

Q: The surface of a hill can be given as h(x, y) = e-(z²+y²), If a ball is placed at the (2, y)…

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Q: Show that for any two vectors u and v: = |

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Q: Prove that in R², the vectors {v1, v2, V3} are always dependent. What about if we have two vectors…

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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.