Question

In: Advanced Math

Let u and v be orthogonal vectors in R3 and let w = 3u + 6v....

Let u and v be orthogonal vectors in R3 and let w = 3u + 6v. Suppose that ||u|| = 5 and ||v|| = 4. Find the cosine of the angle between w and v.

Expert Solution

and are orthogonal vector of then we have

we have to find the angle between and

here

the angle between two vector

so we have to find out and

then we put the value and we got the angle between two vector

Colby Messinger answered 1 year ago

Let u and v be vectors in R3. Consider the following statements.T or F (1) |u ...

Let u and v be vectors in R3. Consider the following statements.T or F (1) |u · v| ≤ ||u|| + ||v|| (2) If au + bv = cu + dv then a = c and b = d. (3) ||u + v||2 = ||u||2 + ||v||2 + 2(u · v) Let u, v, and w be vectors in R3. T or F. (1) u · v − ||u|| (2) (u · v) × w (3) || ( ||u|| projvu ...

2 Let u,v, and w be vectors, where u=(1,2,3,-1), v=(2,3,1,5) and w=(3,5,4,4). 2.1 Construct a basis...

2 Let u,v, and w be vectors, where u=(1,2,3,-1), v=(2,3,1,5) and w=(3,5,4,4). 2.1 Construct a basis for the vector space spanned by u, v and w. 2.2 Show that c=(1,3,2,1) is not in the vector space spanned by the above vectors u,v and w. 2.3 Show that d=(4,9,17,-11) is in the vector space spanned by the above vectors u,v and w, by expressing d as a linear combination of u,v and w.

Let v and w be two nonzero vectors in R4 . Then v and w are...

Let v and w be two nonzero vectors in R4 . Then v and w are linearly independent if only if v is not a scalar multiple of w. True or false?

A) Create two vectors in R3 ( 3D vectors) such that they are orthogonal. b) Using...

A) Create two vectors in R3 ( 3D vectors) such that they are orthogonal. b) Using the two vectors from a) above, determine the cross product of the two vectors c)Is it possible to write the vector [0,0,1] using scalar multiples of these vectors?

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 .

2) Let v, w, and x be vectors in Rn. a) If v is the zero...

2) Let v, w, and x be vectors in Rn. a) If v is the zero vector, what geometric object represents all linear combinations of v? b) Same question as a), except now for a nonzero v. c) Same question as a) except now for nonzero vectors v and w (be care- ful!). d) Same question as a) except now for nonzero vectors v, w, and x (be extra careful!).

If V = U ⊕ U⟂ and V = W ⊕ W⟂, and if S1: U...

If V = U ⊕ U⟂ and V = W ⊕ W⟂, and if S1: U → W and S2: U⟂ → W⟂ are isometries, then the linear operator defined for u1 ∈ U and u2 ∈ U⟂ by the formula S(u1 + u2) = S1u1 + S2u2 is a well-defined linear isometry. Prove this.

Let W denote the set of English words. For u, v ∈ W, declare u ∼...

Let W denote the set of English words. For u, v ∈ W, declare u ∼ v provided that u, v have the same length and u, v have the same first letter and u, v have the same last letter. a) Prove that ∼ is an equivalence relation. b) List all elements of the equivalence class [a] c) List all elements of [ox] d) List all elements of [are] e) List all elements of [five]. Can you find more...

Vector v=(9,0,2) is vector from R3 space. Consider standard inner product in R3. Let W be...

Vector v=(9,0,2) is vector from R3 space. Consider standard inner product in R3. Let W be a subspace in R3 span by u = (9,2,0) and w=(9/2,0,2). a) Does V belong to W? show explanation b) find orthonormal basis in W. Show work c) find projection of v onto W( he best approximation of v with elements of w) d) find the distance between projection and vector v

Determine whether or not W is a subspace of R3 where W consists of all vectors...

Determine whether or not W is a subspace of R3 where W consists of all vectors (a,b,c) in R3 such that 1. a =3b 2. a <= b <= c 3. ab=0 4. a+b+c=0 5. b=a2 6. a=2b=3c