1. Given that the vector u = (x,2) has magnitude 4 and that its direction angle with the positive x- axis is acute, what is the value of x? А. 2 В. 12 С. -12 D. -2/3 Е. 25 F. None of these

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: (3) Suppose a vector x is orthogonal to vectors u and v. Show that x is orthogonal to u+v.

A: We will use the fact that x is orthogonal to u and v to prove that x is orthogonal to u+v also

Q: Show that the lines L1 : x = 4 – t, y = 2t, z = 2+t and L2 : x = 1+ 4t, y = 3 – 8t, z = 5 – 4t are…

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Q: If the magnitude of vector x is 10, y is 21 and magnitude of x-y is 17 what would x+y be?

A: Use the property of magnitudes to solve this problem.

Q: 1or Find. Ewo unit Vectors in X-y plane 30 deyree with the vectur that make angle cf V= 3i +4j ?

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Q: Q1/ If f(x,y)=find a unit vector u for which Duf (2,3) = 0 x+y

A: We have to find a unit vector u for which Duf(2,3)=0 where f(x,y)=yx+y

Q: If p (x, y, z) = x² + y? + z2, what is the unit vector in the direction of Vy (1, 2, 3? )undefined…

A: To find the unit vector in the direction of  ∇φ1,2,3, whereφx,y,z=x2+y2+z2

Q: 8 Find a vector of length: (2) (+) 3 a 10 units which is perpendicular to (a -4 b 3/2 units which is…

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Q: 2 7 Consider the vectors: u = 1 v = -1 w = -2 2 Express W as a linear combination au + bv. What is…

A: follow next step

Q: Let h ( x , y ) = ln ⁡ ( ( x + y ) 2 ) . If you are at the point ( e , e ) what unit vector makes D…

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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: For any two nonparallel and non orthogonal vectors a and b with angle between them, it holds that…

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

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Q: IF A =2âx+4ây , B =-3âx+âz and C =2ây+3âz, the vector in the plane containing A and C and…

A: Given: Let us consider the given values as ,  A→,B→,C→A→=2a^x+4a^yB→=3a^x+a^zC→=2a^y+3a^z

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: 2; Find a vector of magnitude 3 in the direction v = (0, 3, –4)

A: The given direction is 0,3,-4.

Q: O Find a unit vector (a vector with length 1) that has the direction of 3 2

A: Given below the detailed solution

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: The vector which has length 2 and direction opposite to u?

A: We have the given vector as u=-122   We have to find a vector that has length 2 and direction…

Q: If y is orthogonal to the vectors u and v, then y is orthogonal to u+ 3v. True False

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Q: Given: f(x, y) = 3x² – 2y² at (-,0) in the direction from P(-,0) to Q(0,1). . What is the unit…

A: The given problem is to find unit vector of the function in which direction from point P(-3/4,0) to…

Q: Find a set of vectors {u, v} in R* that spans the solution set of the equations w - x -y+ 3z 0, %3D…

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Q: 3. The work Wdone by = xf + 3xyj - (x + z)k to move a particle from point 1 to point 2 is defined by…

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

Q: Find the vector ū which satisfies the given conditions. i =, Ju| = 2 , ū and i have opposite…

A: The unit vector,  , in the direction of the vector is calculated as follows.

Q: 24. Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in Figure 16, and…

A: The vectors v and w are in the x-z plane. The cross product of both vectors will yield a vector…

Q: • We have 2x 2y Vf(x, y, z) = i+ +1)j+6k. x² + y²- 1 x² + y? – 1 | Thus Vf(1,1,0) = 27 + 37 + 6K.

A: We have to show the steps for the above equation.

Q: 6. For the vectors ü = (4, 3) and i= (-2, 3), caleulate the following quantities. (a) la+ 레 (b) la+…

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Q: If u = x2 + 2x -y and v = - 2xy- 2y, then the vorticity vector is - 3yk 10 -yk 110 YK III

A: We have to solve given problem: Concept:

Q: 4. [6.1] If vector b is shown below, sketch a vector. a) Equal to b b) Opposite to b c) With the…

A: Solution of given question is written in below steps.

Q: So if I write the position vector r(t)=OP=, is it correct? or does it has to be r(t)=<x,y,z

A: Solution is here

Q: 1. For what value of c is the vector v = = (2,–5, c) orthogonal to w = (3, 2,9)?

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

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: b) Find the angle (0) between vectors between s = [1, –5, 4] and t = [3,3, 3].

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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: (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: The angle between the two vectors is not equal to Select one: O True O False u= and v= 0= π

A: Here we use the concept of dot product of the vectors.

Q: what is u.v when u and v are two unit vectors with an angle of (pi/6) between them. if u=i and if v…

A: Given: u=i, angleθ between u and v=π6 let's assume v=xi+yjx2+y2 we know that angle between two given…

Q: Rounded to the nearest integer, a two-dimensional vector with length 13 forming an angle of 67.4°…

A: Given:-magnitude of the vector, v→ =13angle with the x-axis, θ=67.4°

Q: 41. Find the value of A if the vectors i+ Aj+3k and-2i+j-4k arc parallel. uectors ii + 3k and 2i -

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Q: b) Find the angle (0) between vectors between s [1, –5, 4] and t = [3,3, 3]. %3D

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Q: Find the second and the third components of a vector n normal to the plane with the equation 7x +…

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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: 22 Given the cross product of 2 vectors u and vis, u x v= -3i-3j+3k, and their dot product is,…

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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: Given that u =, and z = What is the x component of the resultant vector w = Зи + 22

A: Given: u=4,-5z=-11,-10

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: 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: For what values of y are the vectors yi – 2j + 3y k and 6i +j+ 3y k orthogonal.

A: To find the values of y for which the vectors yi-2j+3y k and 6i+j+3y k are orthogonal.