XII. Show that the dual vector of the antisymmetric part of the dyadic (1 2 3) Ā = 4 2 1 (1 1 1) is i^ = &, + &g.

Q: Write down the equations of any two distinct planes with normal vector n = 〈3, 2, 1〉that do not pass…

A:

Q: (1, Find a vector orthogonal to both (3, 2, 0) and to (0, 2, -1) of the form

A: The given question is related with vector space. We have to find a vector orthogonal to both 3 , 2 ,…

Q: To compute h, (x) =*,+0,x,+0,*, in vectorized form then: (theta vector size is 1x3 and X is 3x1) (A)…

A:

Q: 436. The plane that passes through point (4, 7, -1) and has normal vector n= (3, 4, 2)

A:

Q: 2. Determine whether the vectors v, are orthonormal. If not, normalize them to produce an…

A:

Q: If a vector is multiplied by a positive scalar, how is the result re-lated to the original vector?…

A: Explanation:

Q: How do I show that the vectors (1, 2), (0, 1), (-3, 4) are not linearly independent?

A: To verify that the three given vectors in the plane are linearly dependent

Q: Consider the vector v between (-5,5, –3) and (1,1, 1).

A:

Q: The divergence of the vector G = 2i+ sin y j+ 3k is :- -8y + x3 -8y siny + cosy O Option 3 O Option…

A:

Q: Find the components of the vector whose initial point is (2, 2, 4) and terminal point at (0, 2, 0).

A:

Q: What is the scalar projection of á = (1,0, 1) onto b = (0, 3, 4)?

A:

Q: 3. Show that if a particle moves with constant speed, then the velocity and acceleration vectors are…

A:

Q: XII. Show that the dual vector of the antisymmetric part of the dyadic (1 2 3) A = 4 2 1 1 1 1) is…

A:

Q: Find an equation of the plane through the point (4, 5, 1) and with normal vector 6i + j - k. Show…

A: The plane passing through a point A(a) with the normal vector n is given by: r·n=a·n where,…

Q: 3. Give two nonparallel vectors that are both orthogonal to (0, 5, 0).

A: Given A = (0,5,0) Let other two vectors be of type B = (a,b,c) A.B = a.0+b.5+c.0 A.B = 5b For…

Q: The plane with normal vector - 7) containing the point (4,-1,1) has equation Ar + By + Cz = D. If A…

A:

Q: Calculate the integration of (A" - dlP2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector…

A:

Q: Write the scalar equation of the line given the normal vector n =[1,−1] and a point Po (-5,1)

A:

Q: Consider the vector v between (-5, 5, –3) and (1, 1, 1).

A:

Q: Show that if a particle moves with constant speed, then the velocity and acceleration vectors are…

A:

Q: 46. The plane that passes through point (4, 7, -1) and has normal vector n = ( 3, 4, 2)

A: This question can be solved using the concept of equation of plane passing though a point and…

Q: 8. Find the scalar equation of the line passing through the point (1, 5) that has a normal vector…

A:

Q: fx and y are two n-vectors, then prove that 1 1 -+-=1 (Holder inequality) (b) xy, <,, (Schwarz…

A:

Q: The vectors [1, 0, 1], [1, 1, 1] and [1, 0, -1] are coplanar. True False

A: Using coplanarity conditions we have

Q: Obtain a set of orthonormal vectors by Schmidt method: u = (1, 1,0,1), uz = (2,0,0, 1), uz (0, 2,3,…

A: According to gram Schmidt method  orthogonal vectors can be obtained as: x1=u1x2=u2-&lt;u2,…

Q: The terminal point of the vector v = 3i -j+ 5k with initial point (2, 5, -5) is Do not leave any…

A:

Q: 3. find the length of the vector with initial point P(-3,4,1) and terminal point Q(-5,2,2)

A: Solution :

Q: Let = . Let S be the triangle with corners at (3, 1, 2), (3, 4, 2), and (0, 4, 2), oriented away…

A: Given that v→ = 1, 2, 3 and S is a triangle with corners at 3, 1, 2, 3, 4, 2 and 0, 4, 2 oriented…

Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y2 + 2z2 + 4x – 4z = 0.

A:

Q: Obtain a Vector of mayni tude lo that has the same direction as the Vector pPerpendicular toiboth 2…

A: The vector here has a magnitude 10 and perpendicular to both the vectors, 2ax⏞-4ay⏞+3az⏞ and…

Q: Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1)…

A: The line integral ∫CF·dr involves the integration over a specific path. In this problem, the…

Q: Is the set of the three vectors S linearly independent? Explain why. S = 2

A: From the definition, a set S=v1,v2,v3 is said to be linearly independent if the linear combination…

Q: If a vector is multiplied by a positive scalar, how is the result related to the original vector?…

A: Solution:- If a vector is multiplied by a positive scalar, how is the result related to the original…

Q: 3. Show that that the vector u = -5 is a linear combination of the vectors vị = 3 U2 = and v3 %3D

A: Given vectors are u=   2-5  3, v1=  1-3  2, v2=  2-4-1 and v3=  1-5  7   To show that u is a linear…

Q: Show thet direcion vectors of Tue Iae メ-3 レ り+ チ一て Laeメ-コ X-3 ソャ) Z-3 -2 are orthogohal

A: Direction vectors and orthogonality

Q: 3. What is the initial point of vector w if the component form is and the terminal point is (4, 1)?

A:

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, 0, -2), (2, 3, 4) is

A: We will solve the problem

Q: 2) Find the vector from the origin to the center of the sphere 2x² + 2y² + 2z2 + 4x - 4z = 0.

A: The equation of the sphere is, 2x² + 2y² + 2z² + 4x - 4z = 0 So, x² + y² + z² + 2x - 2z = 0 So, (x²…

Q: Find The Steady Sta a vector for tho transiton mutro

A:

Q: Suppose v is a nonzero position vector in xyz-space. How many position vectors with length 2 in…

A: Given that, v is a nonzero position vector in xyz-space.

Q: A particle starts moving from (- 4, 2, 5) so that its initial velocity is 5 î -3 ĵ – 2k and its…

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

Q: State the Cauchy-Schwarz Inequality and use it for solving the two vectors in R³ if = [1,–2,4] and y…

A:

Q: 9. Is the set of vectors {(-2, 2, 0), (1, 1, 1), (8, -4, 2)} over R linearly dependent or…

A:

Q: Find a vector orthogonal to both (-4,5, 0) and to (0, 5, 4) of the form (1,

A:

Q: Find two orthogonal vectors in the plane x + y + 2z = 0. Make them orthonormal.

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: -2 - are the vectors U, = %3D Ug = %3D in M22 are lineor ly depon dent linearly in dependet.

A:

Q: Verify the Cauchy-Schwarz Inequality for the vectors. a = (1, 1, -2), b = (1, -3, -2)

A:

Q: The normal vector of 2x + 3y - z + 5 = 0 is: O [3, -1, 5] O [2, 3, -1] [2, 3, -1, 5] O (-2, -3, 1]

A: Answer :  From question given that the Normal vector form is  ; 2x + 3y - z + 5 = 0

Q: The vector norm is always positive.(i.e. ||X||>0 for every vector X.) Select one: True False

A: We know that The length of a vector with two elements is the square root of the sum of each element…

Q: Find an equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…

A: Given An equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…