Find a unit vector in the plane of the vectors A = i + 2j and B = j + 2k, perpendicular to the vector C = 2i + j + 2k.

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

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Q: Find a unit vector that is orthogonal to both u and v for u = and v = .

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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: snip

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Q: Find the unit vector that has the same direction as the vector v = -i + 2j.

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Q: Determine the two unit vectors that are orthogonal to i = (1,2). Which two unit vectors are parallel…

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Q: Find the B-coordinate vectors of ei and e2, where and B : %3D %3D %3|

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

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Q: When analyzing the vectorĀ = 2i – j + 3k To the sum two vectors, the first is parallel to the vector…

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Q: Find a non-zero vector B' which is perpendicular to A'= 2i'-3j'.

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

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Q: Find the unit vectors that are perpendicular to U = and V =,

A: Given the vectors U→=2, 3, 4 and  V→=-1, 3, -5 We will find the unit vectors that are perpendicular…

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

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Q: Find the angle 0 between vectors u = 2i - jand v = 6i + 4j.

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Q: The unit vector perpendicular to the vectors n1= i-j+3k ,n2=2i+j+3k is a vector?

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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 the angle between the vectors u = /2i - 9j and v =v2i+j-2k.

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

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

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Q: products

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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: find the unit vector u having the same direction as v  v=3j

A: Recall: Formula for unit vector,                  u=v‖v‖

Q: 2.) Find two vectors that are orthogonal to the vector v = 8i - j

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Q: Find the unit vector that has the same direction as the vector v = 3i - 2j.

A: Given vector is v→=3i-2j We have to find unit vector that has same direction as given vector.…

Q: Find two linearly independent vectors perpendicular to the vector 4 v =

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Q: Find a non-zero vector & perpendicular to the vectors v = x = ► 3 H and u = 4

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Q: Are the vectors v = 6i - 3j and w = i + 2j orthogonal?

A: Two vectors are considered to be orthogonal if their dot product is zero.

Q: Find the cross product of the unit vectors. jx i

A: Topic :- Vector

Q: Find the angle between the vector through the origin & the point (1,1,1) and the component of Ā = 2i…

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Q: Find a vector that is perpendicular to both and 2. A =-i - 2j +4k B = 4i - j

A: Take cross product and it's magnitude then find unit vector in perpendicular to both vector

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 the unit vector in the same direction as vv=5i-j

A: Given vector is

Q: Find a unit vector that is orthogonal to both i+j and i+k ?

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

A: Follow the procedure given below.

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

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Q: Decompose v into two vectors Vị and v2, where vi is parallel to w and v2 is orthogonal to w. v - -2i…

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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 two unit vectors that are perpendicular to both j + 2k and i – 2j + 3k.

A: Given that a→=j+2k,  b→=i-2j+3k   We know that the cross product of two vector is perpendicular to…

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 a vector v parallel to u=−7i+j−6k and with magnitude ||v||=12.

A: Given,          A vector v parallel to u=−7i+j−6k and with magnitude v=12.

Q: compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors. What do you…

A: Given: Compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors.

Q: Find the angle between the vectors i + j + 2k and 2i - j +k

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Q: Find a unit vector that is orthogonal to both i +j and i + k.

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Q: Find the unit vector in the direction of v and verify that it has length 1. v = ⟨3 /2, 5/ 2⟩

A: Given vector is v=32,52. To find the unit vector in the direction of v and to verify that it has…

Q: perpendicular to the plane formed by the vectors w1 = [1 2 1] and w2 = [2 2 3], with the z axis

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Q: Find the angle a between the vectors L3] and]

A: Find the angle between vector s

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.