Find a unit norm vector that is orthogonal to both the vector (1,2, –1) and the line of intersection of the planes r + 2y + 2z = 5 and x+ y – 3z = 2.

Q: In Fn, let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

A:

Q: 2. Choose the linearly dependent vectors in R

A: two non zero vectors V1, V2 are said to be linearly independent if and only if aV1+bV2= 0 ⇒ a=0 and…

Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

A: We have, Equation of plane through P0 =(x0, y0, z0) with normal vector n = <a, b, c> Vector…

Q: Determine the constant a so that the vector i = (2x + 3y)î + (2y – 2z)j+ (x + 2az)k is a solenoidal.

A: Given : The vector v→ = (2x + 3y) i^ + (2y - 2z) j^ + (x + 2az) k^.   To determine the constant a so…

Q: Given the vectors ū = (-2, 1, 1) and V = (3, –1, 1), calculate the vector projection of ū onto V

A:

Q: Suppose that the vectors {v, u, w} are linearly independent in some vector space V. Prove that the…

A: Given that the vectors u, v, w are linearly independent in some vector space V. Then the linear…

Q: Find an equation of the plane that passes through the point P(4, 7, 1) and has the vector n = (1, 3,…

A:

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 8V3 and whose components have…

A:

Q: Find a vector of magnitude 2 parallel to the line of intersection of the planes x + 2y + z - 1 = 0…

A: Find a vector of magnitude 2 parallel to the line of intersection of the planes x + 2y + z - 1 = 0…

Q: Verify that the two planes are parallel. -x + 6y + 2z = 8 -x + 3y + z = 9 2. Find the normal vector,…

A: Find your answer below

Q: Find volume V(S) of the parallelepiped S in R3 determined by the (3,4,1); v3 following vectors: vị =…

A:

Q: Find the projection of u onto v and find the vector component of u orthogonal to v. u = ⟨9, 7⟩, v =…

A:

Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: If v and w are two non zero vectors, the vector projection of v onto w is  projwv=v.ww2w Substitute…

Q: Consider the vector v = 1 and the vector "function" w(k) = 1 For what value of k are i and w(k)…

A: Two vectors v→ and w→ are said to be orthogonal if v→·w→=0 Given v→=111w→=11k

Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = Q =…

A:

Q: Decompose the vector v=3i+2j into two vectors v1 and v2, where v1 is parallel to w=2i+j, and v2 is…

A: Decompose v into two vectors v1 and v2,where v1 is parallel to w and v2 is orthogonal to w.v=3i+2j,…

Q: Find an equation of the plane that passes through the point P(4, 6, 3) and has the vector n = (1,6,…

A: I have stated the used formula in the solution.

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = and v =

A:

Q: Find the projection of u onto v and find the vector component of u orthogonal to v.…

A: Given that, u=6,7 and v=1,4

Q: Find a vector parallel to the line of intersection of the planes x+ 3y – 2= =13, and 3x – 4y + = =-8…

A: Solution is here

Q: Define a basis B = (ā,b, c) for R³, where -- 2 6= 1 3 Define P to be the plane spanned by d and b.…

A: To define a basis B=a→, b→, c→, we determine the determinant of matrix formed by vectors a→, b→, c→.…

Q: Find the spacing and involution for the following vector functions 1- ƒ(x, y, z) = (xi + yj + zk]…

A: Topic:- vector

Q: Find a nonzero vector orthogonal to the plane through the points P, Q and R if P(1,0,0), Q(7,8,0)…

A:

Q: M contains the point with coordinates (0,0,1) 2 M is orthogonal to the vector 0

A: Introduction: The general equation of Plane is ax-x1+by-y1+cz-z1=0

Q: Dados los vectores u=2i-3j+4k y v=(4,1,-2) , calcular la norma (módulo) del vector u - 2v V37

A: Given: u=2i-3j+4k v=4,1,-2

Q: Find the equation of the plane E passing through the point P(2,3,1) and parallel to the vectors K =…

A:

Q: ^2

A:

Q: Determine all vectors v that are orthogonal to u.u = (4, −1, 0)

A:

Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = (4,…

A:

Q: Let x 0 and y 0. (a) If xly, show that {x, y} is a linearly independ- ent set. (b) Extend the result…

A:

Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

A: Given, Normal,n=(2,-4,1) Point, P=13,23,1     Find the equation of the plane with normal vector n…

Q: Show that v, = v 2 V2 3 span R and express the vector v= as a linear -7 %3D combination of v,,v2.

A: Solve the following

Q: For two-dimensional vectors u= and v= , then the dot product is simply the scalar obtained by ủ ·…

A:

Q: Find x such that the vectors xi+2j -3k, i+j ,j+3k are Coplanars (lies the Same Plane) . on

A:

Q: The orthogonal projection of the vector v =3i-j+k on the vector b 2i-j+k is

A:

Q: Find a vector w perpendicular to both vectors u=2i-j+2k and v=3j-4k w=i+2j-3k w=-2i+8j+6k…

A:

Q: Let B = {v2, v2, . . . , Vk} be a set of orthonormal vectors, this is, vi vj 0 if i # j and v; · Vi…

A:

Q: Consider the vector y = [1 2 3]. Find the orthogonal projection of y onto the plane x, - 2x2 + 4x3 =…

A: Given vector is y=1,2,3 Given plane is x1-2x2+4x3=0 Normal vector to the p[lane is n=1,-2,4…

Q: Find the weighted Euclidean norm of the given vector. 10 with weights w = v = ||v|| = Ex: 1

A: Here, we need to find the weighted Euclidean norm of the vector v=102 with the weights w=111. Let…

Q: Given the 3-dimensional vectors: A = (xy)i + (2yz)j +(3xz)k B = (yz)i + (2xz)j +(3xy)k Determine the…

A: Here given vectors as A=xyi+2yzj+3xzkB=yzi+2xzj+3xyk

Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( 5 , −…

A:

Q: 6. Let x#0 and y‡0. (a) If x 1 y, show that {x, y} is a linearly independ- ent set. (b) Extend the…

A:

Q: Find basis for the set of vectors in R2 on the line y= nx . where n=9.

A: Explanation of the solution is given below...

Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

A: Given: The maps [0, 1] x [0, 1] to the parallelogram in the XY-plane spanned by the vectors (2, 3)…

Q: Let u= 2 and v= 2. Show that among all the scalar multiples cv of the vector v, the projection of u…

A:

Q: Find a vector that is orthogonal to the plane containing the points P = (3,0, 1), Q = (4, –2, 1) and…

A:

Q: determine projection of the vector b = -1 1 1 on the space generated by the vectors {--E)--[ -[+]}…

A:

Q: 2 -a) Find a unit vector perpendicular to the plane that passes through the points P(1,4, 6), Q =…

A:

Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = ( –…

A: Topic = Vector