Euclidian fpace det R have the inner product X= l1,1) 9nd 1a) Find l , ly || and Lxy>l Describe all vectors (21923) and let y= (5,-1) that are orthogonal to Also Cauchy -Schuarz incquality holds Show for メ= (3,-2) and y= (-d,1)

Q: cost-sint) √2 r(t) = (3e' cost)i + (3e¹ sint)j + 2k For the space curve below, T= i+ sint+ cost s!).…

A:

Q: Parameterize the intersection of z = - Vx² + 7y² _and x² + y? + z? = 200

A:

Q: Two unit vectors that are parallel to the tangent line to the curve y= 2sinx at the point (t/6, 1)…

A: To solve the given question , we must know the slope of the tangent line to the curve y=2sinx at…

Q: Find terminal point Q of vector PQ =    <9, −2, 1>   with the initial point at…

A:

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

A:

Q: IdConsider æ, y, and z real numbers. Identify correctly the following. f:R^3 f(t)=(g(t),h(t),j(t))…

A:

Q: G1 is a semi-circle Y = √4 - X² starting at (2, zero) ends at (-2, zero) while G2 is a directed line…

A:

Q: n+5 c) Let y= and u= Write y as sum of two orth ogon al vector s, one n+4 n-1 is Span (u) and one…

A:

Q: Find orthonormal vectors 91 92 93 in the plane spanned by u = 32 -2,v= 22 2 and w== 973

A: The given vectors, u=32-222, v=-1-441-4, w=-3-273-2. We have to find the orthonormal vectors q1, q2,…

Q: The following vectors are a base that spans a vector space V : al= 2), a2=[ 0 a3= 1 Decide one…

A:

Q: The line through the points the points (xo,Yo, Zo) and (x1,y1, z1) be parametrized by the function T…

A:

Q: If x and y are two n-vectors, then prove that 1 1 (a) x'y< I,l»,- +=1 (Holder incquality) P 9 (b)…

A: Answer :- A) Ans :-

Q: xy² (0) (Use syntax like [3,-4,5] for vectors.) Let F (x, y, z) = xz5 What is the value of curl F at…

A: The vector F(x, y, z) is given. We have to find the value of curl F at (3, 2,1) .

Q: • v, = X,- Lie = 5,-E k V, for 2<psi. k 9 k=1 k Show that vov,=0_for any 1<Q,T<i & Q±T.

A: (Note: There is typo error in question while defining v_{p}. The summation should run k=1 to  p-1,…

Q: Part I. Vector a'(0,1,0), b (1,0,1) calculate (2 points for each question, 10 points in total) (1)a+…

A:

Q: ) Determine whether vectors v,(1,2,1), v2 = (1,0,2) and V3 = (1,1,0) spans the vector space (R³, R ,…

A: Given vectors v1=121, v2=102 and v3=110 We have to determine whether the vectors v1, v2, v3 spans…

Q: Find the domain of the vector functions, ?(?)�(�), listed below. using interval notation. ) ?(?)=⟨…

A: To find the domain of the vector function r(t)=⟨t−3,t2−4​1​,t1/3⟩, we need to consider the values of…

Q: A line l passes through the point P(2,4, 3) and is parallel to the vector (3, 2, –3). | At what…

A: Proceed as shown below

Q: Find the vector equation for the line of intersection of the planes x + y - 4z = 4 and + 4z = -2

A: We have to find the vector equation.

Q: Find ProjS(u) where S is the space spanned by v1= (1/3)(2,1,2) and v2= (1/3)(-2,2,1). Find the…

A:

Q: Let T be a linear transformation from R² to R³ and suppose that (Q)-[]). T ¹ ([³]) - the vector…

A: It is given that,Here we have, Write vectors v1 and v2 in the matrix A

Q: 10) (6 points) Using the inner product (v, w) = 3v¡W1+5v2W2 with the vector space R?. a) Find a…

A:

Q: (a) Give examples of three distinct vectors vị, v2, vz in the vector space R³ such that vz E…

A: Let v1 = {1,1,1}v2 = {2,3,4}v3 = {1,2,3} Here  v2 = {2,3,4} = {1,1,1}+{1,2,3} = v1+v3

Q: Let f,g be scalar functions, ủ be a vector function, and assuming sufficient differentiability. Then…

A: