A a В In the diagram OA = a, OB AB. = b and AP = АВ. a Given that OX = µOP, where u is a constant, express OX in terms of u, a and b. b Given also that AX = 2OB, where 2 is a constant, use a vector method to find the value of u and of 1.

Q: 2) A function is given by f(x, y) = xy - x-4y+4. If Duf(0,0) = 1, find the unit vector directions…

A: According to question,Given function,fx, y = xy - x -4y +4,Du f0, 0 = 1

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

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Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j + 5k 4i + 5j-6k dw (C): If w = tan x…

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Q: Find the unit vector in the direction of v and verify that it has length. v = ⟨−6.2, 3.4⟩

A: Now magnitude is,

Q: In Newton's theory of gravitation, the Earth's gravitational field is given by, -GM r3 where 7 = (x,…

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

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: Let L be the line y = 6 – 4x in R?. Find vectors a and b so that v = a+tb is a vector equation for…

A: Vector equation of line

Q: Given a vector with initial point at P1 and terminal point at P2 given below, find an equivalent…

A: (2,-1) and (3,2)

Q: Find the angle 0 (in radians) between the vectors. (Round your answer to two decimal places.) u = 3i…

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Q: 5. (a) Find two vectors of norm 1 that are orthogonal to the vectors u = (5) and pue (4 E)=

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Q: Find the angle 0 (in radians) between the vectors. (Round your answer to two decimal places.) u = 3i…

A: Given, u=3i+4j and v=-2j

Q: Q2) if the vechrs V=-i +5 and ū=Tz i+5J+2 R Find a) The scalev component of ū in the divection of V…

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Q: Evaluate 1+ x° + y°dS, where S is the helicoid with vector equation т(и, и) — 0 <u < 3, 0 < v< T

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Q: Find the magnitude of the vector v whose initial point is P(5, – 2) and terminal point is Q(0, – 4).…

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Q: A particle is launched from the origin in R^3 with initial velocity v(0) =  and undergoes constant…

A: consider the provided question, v0=0,8,10a=2,-1,-5vx=0, vy=8, vz=10ax=2, ay=-1, az=-5then,…

Q: Find the velocity and position vectors of a particle that has the given acceleration and the given…

A: We have given acceleration, intial velocity and position of a particle we have to calculate velocity…

Q: Given the vector function 7 (t) = (2t, – 2t°, 5t° + 3) Find the velocity and acceleration vectors at…

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Q: Find a non-zero vector & perpendicular to the vectors v = x = ► 3 H and u = 4

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Q: Find a unit vector orthogonal to both u and v.u = i − 2j + 2kv = 2i − j − 2k

A: Given  u = i - 2j +2k = &lt; 1, -2, 2 &gt;v = 2i - j - 2k = &lt; 2, -1, -2 &gt;

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

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Q: For the vector function G(t) = -3cos(2t) i+3sin(2t) j+k, find: dG (b) dt dG (c) G• dt dG dG (d) Gx…

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Q: c) Show that vector ū = 1 cannot be expressed as a linear combination of 2 in R3 3 vectors vi 1 and…

A: we have to show that , we can not write as a linear combination of vectors v1 and v2

Q: (2) For the vectors ä = (-1,3, 4) and 5= (-2,2, 0) calculate the following: (a) ãoË (b) ä x b (c) A…

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Q: Q1: A force of 9 newtons is applied in the direction of the vector from P,(1,0,1) to P2(3,2,0).…

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Q: 1 3 8. For r = , y = |, compute the following: -1 -2 a) I y b) ||r|| c) a unit vector vector in the…

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Q: The vectorr(t) is the position vector of a particle at time t. Find the angle between the velocity…

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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: Find a unit vector perpendicular to i-j and to i +k and with a positive k component.

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Q: 3. Find two unit vectors orthogonal to both j − k and i + j

A: We will find the two unit vectors orthogonal to j-k and I+j as following.

Q: The acceleration of a moving particle in space is given by the vector function a (t) = 3t2 i + 4t +…

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Q: 4. Find the vector equation for a particle if A(t) = 6ti + 12t² j+ k, V(0) = 2i + 3j, and R(0) = 4k.

A: Given that At=6ti+12t2j+k,V0=2i+3j,r0=4k.

Q: 2. Given a force vector F= -381 + 2z + 783 (kg m/s) and the DCM ape CSW = b q n de determine the…

A: Here we solve the given problem.

Q: Given the vector function 7 (t) = (3t, 5t", – 3t° + 2) - Find the velocity and acceleration vectors…

A: Given that vector function r→ t=3t,5t2,-3t5+2 To find the velocity and acceleration at t=-1Solution…

Q: Find the component form of the unit vector obtained by rotating the vector (1.0) 210°…

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Q: Two individuals are attempting to relocate a sofa by applying forces in the indicated directions. If…

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Q: Find the velocity and acceleration vectors in terms of u, and ue. do a0 r= 9 e and :3 dt v=Ju, +Jue…

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Q: Find Vw. w = 6 In V10x² + y² + 4z2 NOTE: Give your answer in unit vector notation; that is, in terms…

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Q: Let ü = (2,1) and i = 5î – 3j. a. Find the angle (in degrees) between the two vectors. Round your…

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Q: If two objects travel through space along two different curves, it's often important to know whether…

A: To solve this we must figure out at what t's positions are equal for each vector component. so, set…

Q: H.W 9- Given that a = (1,1) and b = (-1,0). Find a vector in the same direction as but a+b %3D %3D…

A: Given: a→=1,1, b→=-1,0 To find: A vector in the same direction as but a→+b→ five times as long.

Q: A fish swimming in a horizontal plane has velocity v, = (4.00 î + 1.00 j) m/s at a point in the…

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Q: Find a unit vector that is orthogonal to both i +j and i + k.

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Q: Q2) Suppose a vector y is orthogonal to vectors u and v. Prove or give a counter example that y is…

A: Given that y is orthogonal to vectors u and v. To show: y is orthogonal to vectors u + v or not.

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 addition of the vector using the component methods. 1. 9 m/s [N30°E] and 2 m/s [N 60°E].

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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: r(t) = (te-t 1 1+t2 > Vt2.

A: Given function is  rt=te-t , 11+t2 , tt2-1

Q: Find the velocity and acceleration vectors in terms of u, and ug. do r= 6 e a0 and -= 3 dt Ju, +Juo

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Q: If two objects travel through space along two different curves, it's often important to know whether…

A: Equate the each component of r1 and r2 to find the value of t.