a) Let i = xî + yj + zk, r = |7| and å is a constant vector. Find the value of %3D dxr div

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: Let x be an n-vector. (a) Is it possible for x · x to be negative? Explain. (b) If x · x = 0, what…

A: We shall define, x→=(x1,x2,...,xn) The dot product of two vectors x→ and y→ is given as,…

Q: * Find the values for h for which the vectors are linearly dependent: 7

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Q: a) for which values on are the vectors V3 = 2 %3D 7 19 linearly independent?

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Q: Let x and y be linearly independent vectors in R2.If | |x | |= 2 and | |y | | = 3, what, if…

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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: 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: 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: 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: 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: · Let 2 be the separation vector from a fixed point (x', y', z') to the point (x, y, z), and let z…

A: Since r is the separation vector from the point x',y',z' to the point x,y,z and the difference…

Q: If is a covariant vector in Cartesian coordinates x',x2.

A: In this question, we have covariant tensor (x1x2,x2x1) By using the transformation cartesian to…

Q: Find the initial point A of the vector that is equivalent to (3,7), and whose terminal point is…

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Q: 18 as a linear combination of a and y Express the vector v y.

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Q: 2) If A =,find grad(div A), where r is a position vector.

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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 basis for the set of vectors in R'on the line y = nx. Where n=9.

A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

Q: Find the possible values of x if vectors are j +2k, v =2i + j –- k and w = xi+j - k coplanar: u = i…

A: Given vectors are u=i-j+2k, v=2i+j-k and w=xi+j-k. To find the possible values of x if vectors are…

Q: 4. Show how to find a vector ẽ = c – Ab that's perpendicular to b and is a linear combination of b…

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Q: Give an example of a linear combination that resulted in the zero vector that did NOT have 0's for…

A: Query- Give an example of a linear combination that resulted in the zero vector that did NOT have…

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: What is the most general solution to u + v + w = 1, u − w = 2 in vector form?

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Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

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Q: e vector x²y?

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Q: Find a set of vectors {u, v} in Rª that spans the solution set of the equations w – x + 2y – 4z 0,…

A: The detailed solution is given below Thank you

Q: Find a set of vectors {u, v} in R“ that spans the solution set of the equations 0, 0. w – x – 3z 5w…

A: To find a set of vectors {u,v} in R^4 that spans the solution set of the equations

Q: What are the possible angles 0 between two unit vectors e and f if ||e x f|| V? (Let 0 <o Sn. Enter…

A: The modulus for the cross product for 2-unit vectors e and f are given. The modulus for the unit…

Q: The volume of parallelepiped determined by the vectors u = 2i – k, v = 2j – 3k and .= w = i + j+k is…

A: We use the definition of the volume of a parallelopiped determined by the vectors a, b and c to find…

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

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Q: Show that the vector V = (x+ 3y)i + (y – 32) j+(x – 2z)k is solenoidal. %3D

A: Solenoidal Vector : A vector function whose divergence vanished identically is called a solenoidal…

Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…

Q: Find a set of vectors {u°, v*} in R4 that spans the solution set of the equations w-x-2y+3z=0…

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Q: If U and V are 2 x 1 orthonormal vectors and A = UVT then the trace of A is equal to а. О b. 2 с. -1…

A: We have to find Trace of the Matrix.

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: Find x if the vectors a =i+j+ 2k;b = xi-j+k; coplanar or linearly dependent.

A: Given,       a=i+j+2kb=xi-j+kc=3i-2j-k

Q: Show that the vectors (x1, Y1) and (x, 2) in V, (F) are linearly dependent if

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Q: Which option is equal to the DOT product uV of vectors 3 u = 1 4 -4 26 24 N N

A: The given vectors are: u=314 and v=22-4 Multiply the numbers component wise to find the dot product…

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: IH A and B are any two vectors in V, prove that (A- B) x (A + B) = 2(A X B).

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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: 3. Show (using the concept of vectors) that the area of the triangular region with vectors u 1 and v…

A: Given that, The vectors u and v are the vectors of the adjacent sides of the triangular region.…

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: Þ(x, y, z) = e¬x²-y²-z²+2yz

A: First take gradient and magnitude of gradient

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

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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.