Let u and v be vectors in Rn. Show that 1 1 |||u + v||² − − ||u − v||² . - 4 u. V =

Q: Two vectors u and v in space are if and only if u X v= 0

A: Given vectors in space are u and v The vectors cross product is u x v = |u| * |v|* sin(angle between…

Q: Q5. Are the set of vectors {[0 2 1]",[1 1 1]", [3 2 1]", [3 0 1]"} linearly independent? Does the…

A: Set of vectors are linearly independent if there is no non-zero solution of c1,c2,c3,c4. If there is…

Q: Find a vector b such that |b| = 1/2 that is parallel to a = but with opposite direction.

A: Given that: |b|=12a=<-6, 3, -2>

Q: Let A and B be vectors in R. Show that ||A|| = || B|| if and only if A+ B is orthogonal to Ã- B.

A: To solve the given orthogonality problem related to vector.

Q: Show that (u×v)· w = u ·(v×w).

A: As we know that, Multiplication is an Associative Property, i.e. (a x b).c=a.(b x c) and Sometimes…

Q: ||ī|| = Find the length of the vector = 2 -2 Enter `sqrt(a)' for √Va

A: In this question we will find the Length of the vector.

Q: The vectors 3 -1 1 i = -3 11 10 + k are linearly independent if and only if k +|

A: We will find out the required value.

Q: Suppose that u and v are two vectors with |u| = 1, |v| = 4 and u · v = −2. a. Compute |u + v|. b.…

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Q: Let u and v be vectors in R". Show that ||u – v||? – 2||u – 2v||2 + ||u – 3v||2 = 2||v||? %3D

A:

Q: Find u × v and show that it is orthogonal to both u and v. u = v =

A: Given u→=-1,0,7v→=8,-4,0

Q: Q2 (a) Let n E N and let ở, w e R". Show that if ở · w = 0, then || ở + w||2 = || ||² + ||w||². (b)…

A: This question can be solved using the concept of dot product of two vectors.

Q: Find a vector v such that ||v||=20 and v is in the same direction as 15i+15j.

A: The parallel vector of a vector is the scalar multiple of the vector, and if scalar is positive then…

Q: Find x∈R such that vectors a = and ?=. are equivalent

A:

Q: Prove that the following function is convex over the set of positive vectors: f(x1, x2, x3) =…

A: Given : A function fx1 , x2 , x3=-x1x2+2x12+2x22+3x32-2x1x2-2x2x3. To Prove that the above function…

Q: Find the value of k for which the vectors 2 1 2 and -3 5 k are orthogonal. k =

A:

Q: |3s + 3t Let W be the set of all vectors of the form 3s - 4t. Find vectors u and v in R³ such that…

A:

Q: |Let j and ū = -4 Write j as the sum of two orthogonal vectors, 1 in 9 Span {u} and 72 orthogonal to…

A:

Q: Let a . Find a unit vector in the direction of a = 1 35 i + 5 √35 =j+ k 3 35 X Invalid notation.

A: Let's find unit vector in the direction of a.

Q: Quolel X= -gi +sj -K, Y. i-2 k yo i-2 K Find X x Y

A: (1) Consider the given vectors x=-2i+3j-k and y=i-2k   We have to find x×y   Now, x×y=ijk-2   3-11 0…

Q: Write a in the form of a = a¡T + a„N at t = 0 without finding T and N for r(t) = (2 + t)i+ (t +…

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Q: Suppose u, v are vectors in V. Then ||u – 2v|| = Select one: O a. ||u|| + ||v||' +2Re O b. ||u|| +…

A: Consider u and v are two vectors in V. The objective of the problem is to find the value of…

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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Q: M3. Which of the following expresses the fact that the vectors u and v have the same length? (a) ū -…

A: M3. The two vectors u and v have the same length if: (a)u→·v→=v→·u→