Le and ü .Write j as the sum of two orthogonal vectors, a, in Span {u} and i2 orthogonal to ū.

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: Let y= and u= 3 Write y as the sum of a vector in Span (u) and a vector orthogonal to u.

A: Describe y as the sum of vertices x1 in span u and x2 orthogonal to u         x1=α9, 3=9α, 3α and…

Q: Verify the Pythagorean Theorem for the vectors u and v.u = (1, −1), v = (1, 1)

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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: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: v=2i+4j  and  w=-3i+6j. Now, v·w=2i+4j·-3i+6j=2-3+46=-6+24=18 & w=-32+62=45=35 Therefore,…

Q: Show that if u and v are orthogonal unit vectors then u x v is also a unit vector.

A: To show: That if u and v are orthogonal unit vector, then prove that u×v is also a unit vector:…

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: Let y = 2-| = H and u = Write y as the sum of two orthogonal vectors, ₁ in Span {u} and 2 orthogonal…

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Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: If v and w are two non zero vectors, the vector projection of v onto w is  projwv=v.ww2w Substitute…

Q: Let v = 2i - 5j and w = i - j.Decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

A: v=2i-5j  and  w=i-j. Now, v·w=2i-5j·i-j=21+-5-1=2+5=7 & w=12+-12=2

Q: Show that Il all = 11b|l Are the vectors ã' and b equal?

A: ||a|| = ||b|| a and b are not equal.

Q: Let j = | and ü .Write j as the sum of two orthogonal vectors, it -2. %3D an {u} and ¤2 orthogonal…

A: Given:- →y=-69  →u=5-2

Q: Find all vectors in R* that are orthogonal to both 1 1 V1 = and V2 2 -2

A: Linear Algebra: The vectors are: v1=112-2v2=2112Let denote the vector v3=v1v2v3v4

Q: Decompose V into in two vectors V1 and V2, where V1 is parallel to W and V2 is orthogonal W. V=2i+j…

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Q: Prove that if the vectors a,b parallel, then āxb=0. are %3|

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Q: Prove that two vectors v = (a, b) and w = (c, d)are perpendicularif and only if ac + bd = 0

A: We prove the above statement using the concept of dot product or scalar product of two vectors. The…

Q: The projection of the vector ( i-j+5) onto the vector 2 i+ j + 4 k is

A:

Q: Show that if the vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

A: Given: The vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

Q: Find b so that the vectors v = i + jand w = i + bj are orthogonal.

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Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: To Determine: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w…

Q: Show that the vectors u=, v= , and w= satisfy the following properties of the cross product. и хи30…

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Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: we have to find projwv of the given vectors and then we have to decompose v into two vectors, v1 and…

Q: Determine all vectors v that are orthogonal to u.u = (4, −1, 0)

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Q: Find Projwv and Decompose v into two vectors v1 and v2​, where v1 is parallel to w and v2 is…

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

A:

Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: we have to find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

Q: Determine whether the vectors u= i + 5j − 2k,  v = 3i − j and w = 5i + 9j − 4k are coplanar

A: We have to determine whether the vectors u= i + 5j − 2k,  v = 3i − j and w = 5i + 9j − 4k are…

Q: Suppose ~u and ~w are vectors in R^n . Prove that if ~u and ~w are parallel vectors in the same…

A:

Q: Prove that two vectors v = (a, b) and w = (c, d) are perpendicular if and only if ac + bd = 0

A: we have to prove that the two vectors v=a,b and w=c,d are perpendicular if and only if ac+bd=0

Q: Use the vectors u = a1i + b1j, v = a2i + b2j, and w = a3i + b3j, to prove the given property : u . v…

A: Consider the following vectors: u→=a1i^+b1j^v→=a2i^+b2j^…

Q: Let y = 18 || = and u = 6 Write y as the sum of two orthogonal vectors, ₁ in Span {u} and ₂…

A: Given that                   y→=-4-3 and u→=66.

Q: Let v = 2i - 5j and w = i - j. Decompose v into two vectors, v1 and v2, where v1 is parallel to w…

A: Given vectors are: v = 2i - 5j and w = i - j The formula for the vector projection is given by…

Q: Find the projection of vector u⃗ = −i + 5j + 3k onto the vector v = −i + j − 3k?

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Q: The vectors a and bare unit vectors such that a a+b and 2a +jb are perpendicular. --Determine the…

A: The given vectors a→ and b→ are unit vectors such that a→.b→=12.Given: a→+b→ and 2a→+jb→ are…

Q: 5b- За Let W be the set of all vectors of the form Find vectors i and v in R such that W = span {i,…

A:

Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…

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: Compute the distance between the following vectors: 2 2 w = 3 v = -4 1

A: Hope it is useful

Q: Show that if u + vand ủ – v are orthogonal, then the vectors u and must have the same length

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Q: Let y = and u = 3 Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal…

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Q: . Prove: If a and b are both unit vectors, then axb is a unit vector only when a and b are…

A: since you have asked multiple questions in a single request, we would be answering only the first…

Q: Linear algebra

A: From the given information:Let,

Q: Let y = 185 || 3 and u = Write y as the sum of two orthogonal vectors, ₁ in Span {u} and 2…

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Q: Find the values of ( x ) such that the vectors and are orthogonal.

A: Given: The two vectors are: 3,2,x and 2x,4,x Also, the two vectors are orthogonal.

Q: IH A and B are any two vectors in V, prove that (A- B) x (A + B) = 2(A X B).

A:

Q: Let u and v = .A vector orthogonal to both ú and v is

A:

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

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

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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…