Given that u =< 4,-5 >, and z =<-11, -10> What is the x component of the resultant vector w = Зи + 22

Q: (2) Given u = [2 1 2]T, find a vector v so that the angle between u and v is 60° and the orthogonal…

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Q: Find a unit vector orthogonal to both u and v. u = 8i – 16j + 2k v = 16i + 32j – 6k -

A: In the given question we have to find the unit vector orthogonal to both u and v. u=8i-16j+2k…

Q: Find ||7e – 4f|l, assuming that e and f are unit vectors such that ||e + f|| =

A: Suppose e and f be the unit vectors such that e+f=32 First, find the dot product of the vector e…

Q: (A) Find the vector that is Normal to: A = 2i + 3j +k and such that it is lies in the plane…

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Q: find the acute angle between the given linesby using vectors parallel to the lines. 2 - x + 2y = 0,…

A: 2-x+2y = 0⇒2y = x-2⇒y = x-22⇒y = x2-1             --(1)So, vector parallel to (1) is a→ = 12i ,…

Q: Show that, û . ûm = 0, Use only the fact that û,is a unit vector. Interpret this result.

A: Here we need to prove that dot product of a unit vector and its derivative is zero. Here we use the…

Q: 4. Find the vector v that is orthogonal tou=i+j+k and whose r-component and z-component are 2 and…

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Q: If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, find the angle at…

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Q: find the acute angle between the given linesby using vectors parallel to the lines. y = x, y = 2x +…

A: Here the acute angle between two lines is to be calculated.

Q: Find c so that the vector v is orthogonal to W = ||

A: Given: v=1c. w=2-1 Vector v and w are orthogonal only if the dot product of vectors is zero.

Q: Consider the vector v = (x, 2) in R2. If you rotate the vector by 90-degrees counter-clockwise, then…

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Q: Find a vector v parallel to u=4i−3k and with magnitude ||v||=4

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Q: Find vector u with the magnitude given that satisfies the given conditions. v (7, -1, 3), ||u || -…

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Q: Find the x-component of the vector of length 3 in the direction of V = (-1,-1).

A: v=&lt;-1,-1&gt;=-i-j Unit vector in the direction of vector V i.e.,     v⏜=-i-j(-1)2+(-1)2 =-i-j2…

Q: Find the vector z, given that u = , v = , and w = . z = 8u - 3V - -W 2 1. Z =

A: We have been given the vectors  u = &lt;1, 2, 3&gt; v = &lt;2, 2, -1&gt; w = &lt;4, 0, -4&gt;

Q: What are the possible angles θ between two unit vectors e and f if ||e × f|| = 1/2 ?

A: The cross product of two vectors can be found by the formula a→×b→=a→b→sinθ The magnitude of the…

Q: Dados los vectores u=2i-3j+4k y v=(4,1,-2) , calcular la norma (módulo) del vector u - 2v V37

A: Given: u=2i-3j+4k v=4,1,-2

Q: For what value of t if any, is the vector 5t, 1] parallel to the vector (4, -1) ?

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Q: The vector y which is collinear with the vector u= and satisfies the condition u.v= 3, is O O O…

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Q: Find the cross product of the unit vectors. jx i

A: Topic :- Vector

Q: Is it possible to have ||u−v|| = ||u + v|| if u and v are nonzero vectors? Justify your conclusion…

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Q: At what value of k are these vectors collinear?

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Q: Find the component form of the vector v given ||v|| = 12 following the direction of u (3, –5)

A: Find the component form of the vector v given ||v|| =12 following the direction of u = (3,-5)

Q: Given the points X(1, -2, 1) and Y(0, 3, -2), find a vector that is collinear with XY and has a…

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Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

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

A: Explanation: Given that,  Vectors v and w length is 3 angle between vectors v and w:…

Q: i +j +k andi – j -k.

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

Q: Evaluate /1+ x² + y°dS, where S is the helicoid with vector equation S r(u, v) 0 < u < 3, 0 < v <…

A: Given integral ∬S1+x2+y2dS, where S is helicoid with vector equation r^u,v=ucosv,usinv,v We have to…

Q: Given the points X(1, -2, 1) and Y(0, 3, -2), find a vector that is collinear with XY and has a…

A: Given: X(1, -2, 1) and Y(0, 3, -2).

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: 27-j+4k sī +2j-2k.

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Q: The unit vector normal to the plane 2x + 3y + 6z = 7 is

A: The given plane is 2x + 3y + 6z=7. The unit normal vector to fx,y is defined as n=∇F∇F. The normal…

Q: Find a vector v parallel to u=−7i+j−6k and with magnitude ||v||=12.

A: Given,          A vector v parallel to u=−7i+j−6k and with magnitude v=12.

Q: What is the magnitude of a vector joining two points P(x1, y1, z1) and Q(x2, y2, z2)?

A: The two points  are : P(x1, y1, z1) and Q(x2, y2, z2). As the vector is directed from point P to Q ,…

Q: 2) With respect to the origin 0, the position vectors of points A, B, Cand D are given by OA = 1 OB…

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Q: Evaluate 1+ x² + y*dS, where S is the helicoid with vector equation r(u, v) 0 < u < 2, 0 < v < 2T

A: Given ∬S1+x2+y2dS where S is the helicoid with ru,v=u cos v, usin v, v, 0≤u≤2, 0≤v≤2π. Since ru,v=u…

Q: i. What are the lengths of the x- and y-components of this vector? 10

A: Find your answer below

Q: b) Find out the Vector =y²z?i+x?z?j+z²y²k is irrotational or not?

A: By definition, Any vector is said to be irrotational if the curl of the vector is zero. The given…

Q: Using the vectors from the previous problem, find the projection ul of v onto the vector u and find…

A: We say that 2 vectors are orthogonal if they are perpendicular to each other. i.e. the dot product…

Q: Find a unit vector that is orthogonal to both u and v.       u = −3i + 2j − 5k,    v = i − j + 4k

A: u=-3i+2j-5k,  v=i-j+4k Now the vector orthogonal to both u and v is, w=u×v=…

Q: What is the magnitude of the Vector PQ. P=(1,11) and Q= (9,3)

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Q: (b) Find the values of s such that vectors -si – 2j+ 5sk and 9si + j+3sk are orthogonal.

A: The given vector are -si-2j+5sk and 9si+j+3sk

Q: Find the unit vector in the direction of v and verify that it has length 1. v = ⟨3 /2, 5/ 2⟩

A: Given vector is v=32,52. To find the unit vector in the direction of v and to verify that it has…

Q: Find the sauare of the magnitude of the vector w =u + 2v if u = (8, 2,0) and V = (-1, 1, 2) |wf =…

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Q: Evaluate /1+ x² + y²dS, where S is the helicoid with vector equation т(и, 0) - = 0 < u < 3, 0 < v <…

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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 velocity and acceleration vectors in terms of u, and ug- r= 4 cos 2t and e = 5t

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.