Find a unit vector orthogonal to the vector A= 2i-j+k and parallel to the vectors B= 2i+2j and C= i-j+2k

Q: When analyzing the vector To the sum of two vectors, the first is parallel to the vectorA 2i-j+ 3k…

A: I am attaching image so that you understand each and every step.

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

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Q: The norm of the vector v= - i+10j-8k is ||v||=, (Round your answer correct to 3 decimal places)

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Q: Express the vector in terms of the unit vectors i and j. 2(3, 3) + 3(4, 2)

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Q: Find the unit vector in the direction of v and verify that it has length 1.

A: If vector u is given, then the unit vector in direction of vector u is given as,

Q: Find a unit vector in the direction of v = ⟨−2, 5⟩ and verify that it has length 1.

A: A unit vector in the direction of v = ⟨−2, 5⟩ is given by v/|v|

Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i-2j+ 2k. 1, Find the unit vector…

A: We can solve this as follows:

Q: Determine a unit vector perpendicular to the both vectors A : 2i + 5j – 4k and B - 3i + 6k. |0| = (…

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Q: Find a non-zero vector perpendicular to the vectors and ú =

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Q: 4. Find the vector v that is orthogonal tou=i+j+k and whose r-component and z-component are 2 and…

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

A: Two vectors A and B are said to be orthogonal to each other if and only if their dot product is zero…

Q: Express the vector in terms of the unit vectors i and j. 4) (4,

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Q: Find the given vector : Vector of length 3 in the direction of v = 4i + 3j

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Q: Find a unit vector that has the same direction as the given vector. 4i - j+ 8k

A: Unit vector means the vector whose magnitude is equal to one. So to find the unit vector in the…

Q: Find two unit vectors that are parallel to the yz-plane and are orthogonal to the vector 10i – 2j +…

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Q: A vector of 2 unit length parallel to vector 2i + 2j+k is:

A: We know a vector consists of magnitude and direction as we have to find the direction parallel to…

Q: 4. Find a unit vector in the same direction as the vector 8i- j+ 4k.

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Q: Find a vector v parallel to u=4i−3k and with magnitude ||v||=4

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Q: find the given vector  Vector of length 2 in the direction opposite to v = i − j

A: A vector oppositely directed to v=i-j is is u=-v=-i-j=-i+j                   u=-i+j A unit vector eu…

Q: Find a unit vector in the direction of vector (v= ai + bj ) and orthogonal to the vector ( u= 3i -…

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Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. 1 Find the unit vector…

A: Given, X = -i + 3j  and Y = 4i -2j + 2k

Q: When decomposing the vector into the sum of two vectors the first is parallel to the other vector…

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Q: Find two unit vectors orthogonal to both v (1,1,-1) and w-(2,-1,1).

A: Calculation:Compute the two unit vectors as follows.

Q: Express the vector in the form (a, b). 1(i + j) ji + jl

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Q: Express the vector v =12i -5j as the sum of a vector parallel to b = 3i +4j and a vector orthogonal…

A: here we have to write the vector v in the form: v→=β1+β2Where β1 is parallel to b→ and β2 is…

Q: 2. Find two unit vectors orthogonal to both and .

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Q: 3 Determine the unit vectors that are nernendicular to A - and R -

A: Perpendicular vectors

Q: 2. Express the vector v = 3i – 4j as the sum of a vector parallel to b = 2i +3j and a vector…

A: Given, v→=3i^-4j^ The parallel vector c→ to the vector b→=2i^+3j^ can be written as c→=λb→=2λi^+3λj^…

Q: Find the vector of length v7 in the direction of AB + AC

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Q: Find a unit vector parallel to the vector a´. a'= (-2,3,–1)

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Q: Find a so that the vectors V=i-aj and w=2i+3j are orthogonal

A: Two vectors V and W are said to be orthogonal if their dot product is 0.    V.W = 0

Q: The orthogonal projection of the vector v =3i-j+k on the vector b 2i-j+k is

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Q: Find a unit vector orthogonal to both u and v. u = 31 - 2j - 5k V = +

A: Given: The given vectors are: u=3i-2j-5kv=12i-34j+110k To find: Unit vector orthogonal to both u and…

Q: Find two linearly independent vectors perpendicular to the vector 4 -7

A: This question can be solved using the concept of linearly independent vectors.

Q: Find the length of the vector.v = (0, 1)

A: If Vector V = (V1,V2, V3) then the length of Vector ||V|| = (V1)2+(V2)2+(V3)2

Q: Let u = -2i + 3j, v = 6i - j, w = -3i. Find the specified vector or scalar lu + vl2 - lu - vl2.

A: The given vectors are  u=-2i+3j , v=6i-j  ,w=-3i To find: the value of u+v2-u-v2. Solution: Since,…

Q: ': Find all unit vectors parallel to the and perpendicular to the plane vector V = 5i -j + 2k

A: Here we find all unit vector parallel to the yz plane and perpendicular to the vectorv→=5i∧-j∧+2k∧

Q: Find the two unit vectors orthogonal to both a = (4, 1, 1) and b = (-1, 4, 1).

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Q: Find a unit vector perpendicular to i-j and to i +k and with a positive k component.

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Q: Find a unit vector that is orthogonal to both ı̂ +ȷ̂  and ı̂ +?̂

A: Given query is to find the unit orthogonal vector to the given vectors.

Q: Find a unit Vector orthogonal to both vectors: U =21 +5j-K and V=i+3j-2K.

A: We can find the unit vector as below

Q: Find the two unit vectors orthogonal to both a = 3j + 2k and b = -i- 2k. O A -61 - 2j + 3k and 6i+…

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Q: Find a vector orthogonal to the vectors and

A: This problem belongs to vector section and we solve this using dot product concept

Q: B. Find a vector has length 10 in the direction of vector V=.

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Q: Find a unit vector orthogonal to both u and v. u = -3i - 2j - 5k li 1 3i+ -j + 4 10 V = - 2

A: To find A unit vector orthogonal to both u and v

Q: Express the vectors in terms of their lengths anddirections. i + 2j - k

A: Given:  i + 2j - k

Q: Find a vector 2 units long in the direction of v = 4i - j + 4k.

A: First find a unit vector in the direction of v = 4i - j + 4k.

Q: Find two linearly independent vectors perpendicular to the vector i = |3

A: to find linearly independent vector perpendicular to vector v→=139 solution let X=x1x2x3 as we know,…

Q: Determine a unit vector perpendicular to the both vectors A - 5i + 6j – 8k and B : - 2i + 5k. |0| =…

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Q: Find a vector orthogonal to the vectors ā = and 5=.

A: Recall:  Vector orthogonal to the vectors a→ and b→ is a→×b→a→×b→ We have, a→=1,2,3, b→=1,0,1