Evaluate, don't forget the constant vector, (ri - 2tj + k) dt

Q: Find the unit vector in the direction of v and verify that it has length 1.

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Q: Find a unit vector that is orthogonal to both u and v for u = and v = .

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Q: express vector as a product of its length and direction. 1/(3)^1/2 i + 1/(3)^1/2 j + 1/(3)^1/2 k

A: Let the given vector is: v=13i+13j+13k

Q: Find the unit vector in the direction of v and verify that it has length 1.

A: If vector u is given, then the unit vector in direction of vector u is given as,

Q: The curd of the vector funchion v = Jx i+ Jgj+ ZK is ☺ xi+ yj+ zK

A: It is given that, v→=x i^+y j^+z k^   According to curl, the swirl of a vector around a point. It is…

Q: What is the zero vector?

A: We have to define

Q: Let v be the vector from initial point P1 = (-7, -4),to terminal point P2 = (0, -2). Write v in…

A: Vector u from (a,b) to (c,d) is (c-a,d-b) or  (c-a)i+(d-b)j

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: Solve numerically for The scalar projection of vector u onto v

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Q: Let v be the vector from initial point P1 = (4, -5), to terminal point P2 = (4, 3). Write v in terms…

A: Let v be the vector from initial point P1 = (4, -5), to terminal point P2 = (4, 3). To write v in…

Q: Find the parallel projection of the vector v = onto the vector w=.

A: Given problem:- Find the parallel projection of the vector v=<4, -5, 7> onto the vector…

Q: Find a unit vector that has the same direction as the given vector. 4i - j+ 8k

A: Unit vector means the vector whose magnitude is equal to one. So to find the unit vector in the…

Q: Find a-Vectak S unit, tengte inthedirectionofthe Vector A-ixjtk-

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Q: is The unit vector in the direction of v=(4,0,–3)

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Q: What is the i-component of unit vector of the vector u ? Give your answer correct to two decimal…

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Q: Let v be the vector from initial point P1 = (-3, 4) to terminal point P2 = (6, 4). Write v in terms…

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Q: What is the definition of the triple scalar product for vectors u, v, and w in ℝ3?

A: To Define: Scalar Triple Product for vectors u, v and w in ℝ3.

Q: Express the vector in the form (a, b). 1(i + j) ji + jl

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Q: Let b be the vector of length 35 that when drawn in standard position makes a 290° angle with the…

A: Given : length of vector b=35 ⇒b=35 Also, b makes angle 290° with positive x axis. So, b=b1i+b2j,…

Q: Evaluate F - dS, where F = and S is the helicoid with vector equation r(и, о) - = 0 < u < 2, 0 < v…

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Q: Let v be the vector from initial point P1 = (2, -1) to terminal point P2 = (5, -3). Write v in terms…

A: Given that v is the vector that has initial point P1 = (2, -1) to terminal point P2 = (5, -3).  we…

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: Let v be the vector from initial point P1 = (-8, 6), to terminal point P2 = (-2, 3). Write v in…

A: Let v be the vector from initial point P1-8,6, to terminal point P2-2,3.

Q: Find a unit vector that has the same direction as  4i − j + 8k.

A: we have to find a unit vector that has the same direction as 4i-j+8k let the given vector be a→…

Q: Let a be the vector of length 114 that when drawn in standard position makes a 165° angle with the…

A: Given:- Length of the vector, v= 114, angle is 1650Vector in component form:-(a1, a2)a1=v cos θa2=v…

Q: and the unit vector along the direction of u.

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Q: Find a unit vector orthogonal to both u and v. u = 31 - 2j - 5k V = +

A: Given: The given vectors are: u=3i-2j-5kv=12i-34j+110k To find: Unit vector orthogonal to both u and…

Q: e vector x²y?

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Q: Find the projection of vector u⃗ = −i + 5j + 3k onto the vector v = −i + j − 3k?

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Q: Find a unit vector that is orthogonal to both ı̂ +ȷ̂  and ı̂ +?̂

A: Given query is to find the unit orthogonal vector to the given vectors.

Q: Find a non-zero vector 7 perpendicular to the vector u = 5= [8]. 6

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Q: Calculate and display the error vector & and use it (c) to provide an orthogonality check on your…

A: Given: The set of data points, x y z 0 0 4 1 0 4 0 1 4 1 1 0 To plot them on a set of…

Q: Describe all vectors v that are orthogonal to u

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Q: Find a unit vector u in the direction of v. Verify that llull=1 v=(15,0)

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Q: Express the vector H %3D p?za, + зфzaф - рф*а, at B(3, -4, 1), in CCS.

A: The given vector is H→=ρ2z aρ+ 3Φz aΦ - ρΦ2 aZ.We have to express it in the cartesian co-ordinate…

Q: Q3. Prove that (only one): ax-V3ay a- is a unit vector? b- A = 6ax – 3a, + 2a, and B = 3ax + 2a,y –…

A: Given two statements . We need to prove only one out of that  So, here we will prove first statement…

Q: find a ptenttal fncAren for the vector fteld. 2 2 .3

A: Given function is fx,y,z=6x2y2,4x3y+16y3z2,8y4z-7 Take, ∂f∂x=6x2y2…

Q: Let v be the vector from initial point P1 = (-3, 0) to terminal point P2 = (-2, -2). Write v in…

A: Solution:- we have to find vector v in which  initial point P1 = (-3, 0) to terminal point P2 = (-2,…

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 a unit vector u in the direction of v = 〈6, -1〉. Verify that ⎥⎥ U⎥⎥ = 1

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Q: Let v be the vector from initial point P1 = (4, -5) to terminal point P2 = (4, 3). Write v in terms…

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Q: Assuming vector B is 12 units long, vector 4B is:

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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: Let vector u = and vector v . Find the magnitude of 3u-4v. Round to one decimal place.

A: Let vector u= &lt;3, 4&gt; and vector v = &lt;6, 7&gt; then find the magnitude of vector 3u-4v.

Q: Express in Cartesian components: (a) the vector at A(4, 40°, -2) that extends to B(5, -110°,2); (b)…

A: express in cartesian components (a) the vector at A4,40°, -2 that extends to B5,-110° , 2 (b) a unit…