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

Q: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar

A: We can check whether the three vectors are co planar  or not as below

Q: Given that p and r find in column vector form:

A: In this question, we find the column vector by using the given vectors.

Q: If vector u=2i+3j+4k is orthogonal to vector v=3i+2j-bk, then value of b is 4 1 2 3

A: Two vectors x , y  are orthogonal or perpendicular if x·y=0

Q: Find linearly independent vectors which generate al lutions of Ax = 0.

A:

Q: Why are there no vectors u and v in R,, such that ||u.||= 2, ||v|| = 3, and    uxv= -7?

A: The given values are, u=2, v=3,   and  u×v=-7. The objective is to find the valid reason for the…

Q: Show that, in an inner product space, there cannot be unit vectors u and v with <u, v > <…

A:

Q: 23. Show that u + v < u + v for any vectors u and v.

A:

Q: Assume that the vectors u = ai-j+k and w=i+9j+5k orthogonal. Then the are value of a is

A: If two vectors are orthogonal (perpendicular), then their dot product is 0. We use this to solve the…

Q: Solve numerically for The scalar projection of vector u onto v

A:

Q: Prove that u is orthogonal to v - proju(v) for all vectors u and v in Rn, where u ≠ 0.

A:

Q: In general, show that the vectors V = ai + bj and W = -bi +aj are always perpen-dicular. Assume a…

A: Given vectors are v=ai+bj and w=-bi+aj, where a≠0 ,b≠0. We know that two vectors are perpendicular…

Q: Let y = and u = Write y as the sum of two orthogonal vectors, y, in the span of u, and y, which is…

A: Solution

Q: Suppose that uj and u2 are orthogonal vectors, with u1 = 2 and u2|| = 4. Find |5u1 - u2 ||. ||5u1 -…

A: We have to solve given problem: Let  U1=(a1,a2)  U2=(b1,b2)5U1-U2=5(a1,a2)-(b1,b2)…

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: The scalar projection of vector A onto another vector B will be the negative of that scalar…

A:

Q: 4

A: We are given the following vectors.

Q: The length of the cross product between the vectors j and -j is equal to the zero vector. Select…

A: Solutions

Q: Compute the distance between the vectors u = and v = 315

A:

Q: 2. If a --i+3j-k and E-2itj-3K decompose vectoes E into the sum of two vectors, one is paralled and…

A: This question can be solved using the concept of condition of two vectors to be parallel and…

Q: Show that if u and v are n-vectors, then u · v = uT v.

A: Consider the n vectors  u=u1u2u3.un,v=v1v2v3.vn

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: (B) Show that the area of triangle is - ÁxB (Using Vector method)

A: Let, a parallelogram be:

Q: Verify the Cauchy-Schwarz Inequality for the vectors.u = (6, 8), v = (3, −2)

A:

Q: 10) Find two vectors of norm 1 that are orthogonal to the vectors u = and

A: Consider the provided question, u=12-23 and v=2134 Let w=ABCD be such a vector,Then, w·u=0…

Q: Find unit vectors that satisfy the stated conditions.

A: I have provided this answer with full description in step-2.

Q: Show that there are no vectors u and v such that llull = 1, llvll = 2,and u·v= 3.

A:

Q: The terminal point of the vector v = 3i +5j – 4k with initial point (2, –1, 4) is

A: Follow next step

Q: Compute the distance between the vectors u = and

A: Given vectors are u=42−16 and v=4315. We have to find the distance between the vectors u→ and v→.…

Q: Let x and y be two orthogonal vectors. Then prove that +

A:

Q: If x, y are two no vectors, then prove that |xty | || X lle y llq by = + // use Holder inequality.

A:

Q: Show that the vectors do not span R' by giving a vector not in their span.

A: Solution :-

Q: If ï = (, 2), find a vector i that is perpendicular to ū.

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: 9. Show that for any real numbers a and b the vectors u = ai and v = bj are orthogonal?

A: Topic:-  vector algebra

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

A:

Q: . Let x and y be two orthogonal vectors. Then prove that

A: If x is any vector then Euclidean norm or 2-norm is denoted by ||x||2 and is given by  ||x||2 =…

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: Find two vectors of norm 1 that are orthogonal to the vectors u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2)…

A: Let X=x,y,z,t be the vector that is orthogonal to u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2) and w= (3,…

Q: For the vectors u = (-4,1) and v = (-2,3), calculate projyu and scal, u. projyu = OD

A: Here I am attaching image so that you understand each and every step.

Q: Suppose that u, and uz are orthogonal vectors, with ||u1|| = 5 and ||u2|| = 2. Find ||4u1 - u2||- ||…

A: Let,        u=x1i+y1j+z1kand v=x2i+y2j+z2k It is given…

Q: Write y as the sum of two orthogonal vectors, x1 in Span{u} and x2 orthogonal to u

A:

Q: ind a vector orthogonal to both u and j+k. u=2i-j+3k

A: we have been given two vectors,  u = j+k. v=2i-j+3k   the unit vector that is orthogonal to both…

Q: Prove that swapping the order of vectors in the cross product changes the sign of the output: ьха3 -…

A:

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

A:

Q: prove that 1 Ə div A; = {√g grk Ak} = div A¹, Əx* where A; and Ai are the covariant and…

A:

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

A:

Q: b) Show that the vector w = u – proj,u is orthogonal to proj, u

A: The expression for the vector projection of u onto v is: projvu=v·uv2v Given: u=3,4,0 and v=-2,3,-6…

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.