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

Q: Find three mutually orthogonal unit vectors in R° besides +i, ±j, and tk. 3

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Q: Decompose v into two vectors,one parallel to w and the other orthogonal to w. ; v=-i+2j; w=3i-j

A: Given: Decompose v into two vectors,one parallel to w and the other orthogonal to w.  v=-i+2j;…

Q: Find a unit vector normal to the plane containing v=2i+3j-k and . w = -2i - 4j - 3k.

A: Given: v=2i+3j-k  w = -2i - 4j - 3k.

Q: Find a unit vector orthogonal to both u and v. u = 8i – 16j + 2k v = 16i + 32j – 6k -

A: In the given question we have to find the unit vector orthogonal to both u and v. u=8i-16j+2k…

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar 6v

A: Given: The vectors u = 2i - 5j, v = -3i + 7j, and w = -i - 6j

Q: Determine whether the vectors a = 2i − 3j + 5k, b = 3i + j − 2k and c = i − 7j + 12k are linearly…

A: We have to solve given problem:

Q: Find the Euclidean inner product of the given vectors. 3 4 u = v = (u, v) = Ex: 5

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Q: 3. Find the angles between the vectors: u = 2i + j, u = 2i – 2j + k, v = 3i + 4k a. v = i + 2j – k…

A: a.)u=2i+j , v=i+2j-klet θ be the angle between the…

Q: 4. Find two unit vectors orthogonal to both j-k and i+j.

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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: Determine if the given vectors are coplanar u = 2i - j - k; v = 4i + 3j + 2k; w = 6i + 7j + 5k

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Q: 3. Find the angles between the vectors: u = 2i + j, v= i + 2j – k а. b. u = 2i – 2j + k, v = 3i + 4k

A: Angle between two vectors, θ=cos-1u→.v→|u→| |v|→ a)  u→.v→=2i+j.i+2j-k       =2+2 u→.v→=4 |u→|=22+12…

Q: Determine whether the vectors cosx, 1, and sin2(x/2) are linearly independent in C[−π,π].

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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: Find the weighted Euclidean inner product (u, v) = -3v1 u1 – 3vzuz of the given vectors. u = (u, v)…

A: Given u, v=-3v1u1-3v2u2 u=-3-2, v=14

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar v - u.

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Q: Let u = -i + j, v = 3i - 2j, and w = -5j. Find the specified scalar or vector: 4u.(5v - 3w)

A: Given: u = -i + j, v = 3i - 2j, and w = -5j

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: 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: Find a unit vector orthogonal to both u and v.u = i − 2j + 2kv = 2i − j − 2k

A: Given  u = i - 2j +2k = < 1, -2, 2 >v = 2i - j - 2k = < 2, -1, -2 >

Q: Find the possible values of x if vectors are j +2k, v =2i + j –- k and w = xi+j - k coplanar: u = i…

A: Given vectors are u=i-j+2k, v=2i+j-k and w=xi+j-k. To find the possible values of x if vectors are…

Q: Find a unit vector orthogonal to both u and v. u = 8i - 16j + 4k v = 16i + 32j – 12k

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Q: Find the weighted Euclidean inner product (u, v) = 2v1u1 – 4v2 U2 of the given vectors. 3 4 V = u =…

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Q: Calculate the scalar triple product u · (v × w) of the vectors u = 3i−2j−5k, v = i + 4j−4k, w = 3j +…

A: Given:  u = 3i−2j−5k, v = i + 4j−4k, w = 3j + 2k

Q: Show that v, = v 2 V2 3 span R and express the vector v= as a linear -7 %3D combination of v,,v2.

A: Solve the following

Q: Determine whether the vectors v, = 1 10 and 11 are linearly %3D V3 independent.

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

Q: Find a unit vector orthogonal to both u and v. u = i + 2j v = i+ 3k

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Q: Let u = -2i + 3j, v = 6i - j, w = -3i. Find the specified vector or scalar 3u - (4v - w).

A: Given- u=-2i+3j,v=6i-j and w=-3i To find- 3u-4v-w

Q: Determine whether the vectors a = 2i-3j+ 5k, b 3i+j-2k and c=i-7j+12k are linearly dependent or…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Let v = 2i + 4j and w = -2i + 6j. Decompose v into two vectors, v1 and v2, where v1 is parallel to w…

A: v=2i+4j  &  w=-2i+6j Now, v·w=2-2+46=20 & w=-22+62=40 Now,…

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

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Q: Find the triple scalar product (u xv) •w of the given vectors. u= - 5i – 3j + 4k v = 9i – 10j + 7k w…

A: Given that      u = -5i-3j+4k     v = 9i-10j+7k     w = 9i-7j-3k Here we have to find the value of…

Q: Use vectors =(-1, 1), v= (7, –2), and w= (0, 4) to find (u w)v, and determine whether the result is…

A: We can answer it as below

Q: Find a unit vector orthogonal to both u and v.u = 7i − 14j + 5kv = 14i + 28j − 15k

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Q: Find the vector projection of vector u onto vector v, and find the vector component of u orthogonal…

A: The projection of vector u onto v is given by projvu=u⇀v⇀v⇀2v⇀

Q: Let a = 2i and b = -2i + 3j be two-dimensional vectors. Compute la – b|.

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Q: 4. Determine whether the vectors a = 2i – 3j+ 5k, b = 3i+j – 2k and c =i- 7j +12k linearly dependent…

A: To check whether the vectors are linearly dependent or linearly independent.

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar 5v.

A: Consider the given vectors u=2i-5j , v=-3i+7j , w=-i-6j

Q: Let u = -i + j, v = 3i - 2j, and w = -5j. Find the specified scalar or vector: 5u.(3v - 4w)

A: Given: u=-i+j, v=3i-2j and w=-5j

Q: Find a unit vector orthogonal to both u and v. u = 2i – 5j + 3k 1 V = -k + 10

A: Please go through the attached solution. I hope that it  will help you .Thankyou . Best regards.

Q: Find a unit vector orthogonal to both u and v. u = i + 2j + 2k v = 2i +j – 2k

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Q: Find a unit vector that is orthogonal to both u and v.       u = −3i + 2j − 5k,    v = i − j + 4k

A: u=-3i+2j-5k,  v=i-j+4k Now the vector orthogonal to both u and v is, w=u×v=…

Q: State whether the vectors are parallel, orthogonal, or neither. 5) v = 2i + j, w =i- 2j 6) v = 2i +…

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Q: Calculate the triple product u · (v × w) of the vectors u = 3i − 2j − 5k, v = i + 4j − 4k, w = 3j +…

A: Calculate the triple product u · (v × w) of the vectors u = 3i − 2j − 5k, v = i + 4j − 4k, w = 3j +…

Q: Decompose v into two vectors, v, and v2, where v, is parallel to w and v, is orthogonal to w. v =…

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