1. Vector u =< 0,−1,3 > is given. Find a non zero vector v which is...

1. Vector u =< 0,−1,3 > is given. Find a non zero vector v which is perpendicular to u. Then ﬁnd a vector w which is perpendicular to both u and v. Explain the reason for your selection clearly.

2. Find the slope of the tangent line to the parametric curve x = 5 + sin(3θ) and y = −3 + 2tanθ at θ = π.

Expert Solution

milcah answered 2 years ago

Prove that if U, V and W are vector spaces such that U and V are...

Prove that if U, V and W are vector spaces such that U and V are isomorphic and V and W are isomorphic, then U and W are isomorphic.

let v and u are random variables fvu(v,u)= e^-v-u for u ,v>=0 Z= e^v+u find fz(z)...

let v and u are random variables fvu(v,u)= e^-v-u for u ,v>=0 Z= e^v+u find fz(z) ?

(1) Suppose that V is a vector space and that S = {u,v} is a set...

(1) Suppose that V is a vector space and that S = {u,v} is a set of two vectors in V. Let w=u+v, let x=u+2v, and letT ={w,x} (so thatT is another set of two vectors in V ). (a) Show that if S is linearly independent in V then T is also independent. (Hint: suppose that there is a linear combination of elements of T that is equal to 0. Then ....). (b) Show that if S generates V...

A non-uniform b-spline curve knot vector is given as (-1, -1, -1, -1/2, 0, 0, 0,...

A non-uniform b-spline curve knot vector is given as (-1, -1, -1, -1/2, 0, 0, 0, 1, 1, 1, 3/2, 2, 2, 3, 3, 3, 3). Show the equation diagrammatically and sketch the curve with their respective control polygons if the curve is cubic (degree 3, order 4).

Consider the surface S described by r(u,v) =〈2 cosusinv,3 sinusinv,4 cosv〉,0≤u≤2π, 0≤v≤π, and consider the vector...

Consider the surface S described by r(u,v) =〈2 cosusinv,3 sinusinv,4 cosv〉,0≤u≤2π, 0≤v≤π, and consider the vector field F(x,y,z)=〈−2x,y,z〉.(a) Sketch or name S. (b) Set up (DO NOT EVALUATE) ∫ ∫S F·n dS over S. (c) Using the divergence theorem, deduce the value of the surface integral.

1,Let v=(1,1)v=(1,1) be a vector in the xy-plane. Find a planar vector w which has length...

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Let U and V be vector spaces, and let L(V,U) be the set of all linear...

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Let V be a vector space and let U and W be subspaces of V ....

Let V be a vector space and let U and W be subspaces of V . Show that the sum U + W = {u + w : u ∈ U and w ∈ W} is a subspace of V .

Find a unit vector that is orthogonal to both u = i − 4j + k and v = 2i + 3j.

Given vector s = [4, -5, 7], u = [-6, 8, 11], and v = [-5,...

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