Suppose di ,de,..do ore distinct real numbecs det Prove ė lineerle fade pendent ere vectors in c^(R).

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

A:

Q: Find the plane equation through point (3, -1, 7) and perpendicular to normal vector n = (4, 2, 5)

A:

Q: Prove that llu - vll >=llull -llvll for all vectors u and v in Rn.

A: According to the given information, it is required to prove the inequality.

Q: Find the shortest distance from point P = (1,2,-3) to the plane which passes through (2,3,-1) and…

A:

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

A: Explanation:

Q: 2. 1 show thet vectors cre linecrly dependent or lineerly in dependont

A:

Q: Show that no linearly independent set of vectors can contain the zero vector.

A:

Q: Prove that u · v = 1/4 llu + vll2 -1/4llu - vll2 for all 4 4 vectors u and v in Rn.

A: Given Data The equation to prove is u∙v=1/4||u+v||²-1/4||u-v||².   Evaluate the right hand side for…

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

A:

Q: what is the parametric and symmetric eqvotions of the line that passes thrs point (4.-3,57 to beth…

A:

Q: Find the vector projection of (3, 3, 4) onto (–1, -2, 2).

A: Projection of u onto v is given by.

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

A:

Q: find the diJ tance betueen the vectors

A:

Q: It is possible for two nonzero vectors to have a dot product of 0. True False

A: Let u and v be two nonzero vectors

Q: The usual absolute value on the real numbers is a vector norm. Select one: True False

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

Q: The vectors in Z22 are [ O, O] , [ O, l], [l, O ], and [l, l ]. (How many vectors doesZn 2 contain,…

A:

Q: Suppose e vectors. that a and b ave nonzero Under what ciraumstarces is comp= compas Under ahat…

A: According to the problem, we have

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

A:

Q: Give a vector of length 13 that is parallel to (-1,2, –2).

A: Topic- vector calculus

Q: wing vector fields is not con

A:

Q: Give an example of a non zero vector that is perpendicular to (5,7,4)

A: We know that "two vectors are perpendicular to each other if and only if their dot product is zero"…

Q: A vector orthogonal to the plane through the poii (-1,0,0), (0, –2, –2), (2, 3, 4) is < -2, – 10, 9…

A: The given 3 points are A (-1,0,0) , B (0,-2,-2) &amp; C (2,3,4) Let, x1=-1, y1=0, z1=0 x2=0, y2=-2 ,…

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

A:

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

A:

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

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

Q: Find the angle between the vectors (4, 2) and (7, -2). Carry your intermediate computations to at…

A: solve the following

Q: The plane with normal vector (4, 6, 7) containing the point (-5,-1,5) has equation Ax + By + Cz = D.…

A:

Q: Suppose that Tui, Tus As lineady independent (Here, TELLU, W)) Prove that vi, Vz is linearly…

A:

Q: five vectors in Span v1, V2}. Do not make a sketch. 8 - -

A: In this question, the concept of the span of the vector is applied. Span The smallest linear…

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: Determine whether Hhe Lindependent. by inspection Vectors are linearly 6. -2 -3

A: A vector is given

Q: Find the unit vector along the line joining point (2, 4, 4) to point ( - 3 , 2, 2). A) -0.8703ax -…

A: We can solve this as follows:

Q: Prove that llu + vll2 + llu - vll2 = 2llull2 + 2llvll2 for all vectors u and v in Rn

A:

Q: Show that there are infinitely many vectors in R^3 with Euclidean inner product with (1,-2,4)is zero

A: Given vector is (1,-2,4) in R^3

Q: Represent the line segment from P(−2, −3, 8), Q(5, 1, −2) by a vector-valued function and by a set…

A: Represent the line segment from P(−2, −3, 8), Q(5, 1, −2) by a vector-valued function and by a set…

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: 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: Sketch planeglven by Iz-31 = 1Z + lomplen the Cunve in the |ス-3| - |N+3i| 2. 2. 2. =フナ

A:

Q: what will be four forms of dot product for two vectors A and B by defining their metric tensors?

A: Dot product of two vectors is given by the product of the magnitudes an cosine of the angle between…

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: Is the line passing through the point (3/2, 1) and slope −2 a hyperplane ? If yes, identify this…

A: Any line in 2D is a hyperplane.  ax+by=c, is a hyperplane (a,b) is called the normal vector  c is…

Q: Suppose there is a collection of three or more two- dimensional vectors. Provide an argument…

A: Collection of two dimensional vectors mean those vector having i and j components.

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

A:

Q: to Dara bala y=XZ. Find the unit vectors that are parallel to the tangent line Dara bola y = x² at…

A:

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

A:

Q: Find the unit vectoru in the di rection of the vectorv=3(2, 2, 1).

A: