If a = i+ 2j +k and b = i+10j + k, find a unit vector with positive first coordinate orthogonal to both a and b. i+ j + k

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

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Q: If a = i+ 3j +k and b = i+ 9j +k, find a unit vector with positive first coordinate orthogonal to…

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Q: If v = -2i + 5j, find a vector orthogonal to v.

A: Given v=-2i+5j We need to find a vector that is orthogonal to v. Two vectors are said to be…

Q: If u is a unit vector and a is a positive scalar satisfying au + = 0, find a and u.

A: If u is a vector and a is positive scalar satisfying   au+1,-2,5=0.  To find : a and u.

Q: Find the vector with the given length || v || = 3, and in the direction of u = (0,2,1, -1)

A: Sol

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 the unit vector in the direction of v and verify that it has length. v = ⟨−6.2, 3.4⟩

A: Now magnitude is,

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

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Q: If a = i+ 4j + k and b =i+ 8j +k, find a unit vector with positive first coordinate orthogonal to…

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Q: 4. Find a unit vector that points in the same direction as v = (1,3,9).

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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: 13. Show that the pair of vectors i + i and i – i is perpendicular.

A: Two vectors is said to be perpendicular if their scalar product is zero.

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A: We know that two vectors u and v are said to be orthogonal if their dot product u . v = 0. Given…

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, –1)

A: the given vectors are: u=-8,-6,4v=17,-18,-1 we have to find a unit vector that is orthogonal to both…

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 vectors that are orthogonal to the vector v = 8i - j

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Q: The vector from the origin to point A is given as (-2, -4, 5) and the unit vector directed from the…

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Q: Find the vector v with the given length and the same direction as u.||v|| = 3, u = (0, 2, 1, −1)

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Q: find the given vector. Unit vector in the direction opposite to v = (−4, 4, 2)

A: Given, v=-4, 4, 2

Q: Find a unit vector that is orthogonal to both u and = (-8, -6, 4) v = (17, -18, -1)

A: In this question we will use basic of calculus i.e vector calculus. We will simply find the cross…

Q: If a = i+ 2j + k and b = i+ 5j +k, find a unit vector with positive first coordinate orthogonal to…

A: Given that     a = i+2j+k and b = i+5j+k We have to find a unit vector with positive first…

Q: Determine a unit vector perpendicular to both A=i+2j-3k and B=-2i-3j+k

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Q: If a = i+5j + k and b = i+ 9j +k, find a unit vector with positive first coordinate orthogonal to…

A: We have to find

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: 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 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: Find the vector with length V17 and same direction as i= (7,0, –6).

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Q: Find three mutually orthogonal unit vectors in ℝ3 besides ±i, ±j, and ±k.

A: Vector: At first we can take a=<1,1,1> The second case we can take b=<0,1,-1> The…

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: If a = i+ 10j + k and b = i+ 11j+ k, find a unit vector with positive first coordinate orthogonal to…

A: Vector cross product of given two vector  is orthogonal to two given vector

Q: If ï = (, 2), find a vector i that is perpendicular to ū.

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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 that is orthogonal to both u = (2, -8, 6) and v = (4, 10, -6).

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Q: Given that a = (-10,9,13) and b = (14,–6,12), а. i) ii) compute the dot product. find a vector…

A: (i) Given  a→=-10i→+9j→+13k→b→=-14i→-6j→+12k→ Then,  a→.b→=-10i→+9j→+13k→.-14i→-6j→+12k→…

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: If the magnitude of the vector u is √2 and its direction is 225°, then its components are:   (1,…

A: Solution of question as follows

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

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

A: Given:  i + 2j - k

Q: If a = i+ 3j + k and b = i+9j + k, find a unit vector with positive first coordinate orthogonal to…

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Q: Find two unit vectors that are orthogonal to both u = -7i+ 3j + k, and v= 2i + 4k

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Q: Assuming vector B is 12 units long, vector 4B is:

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Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) (10, -12, -2) %3D V =

A: Find the unit vector that is orthogonal to both u and v

Q: Find a unit vector that has the same direction as the given vector. ‹-3, 3, 4›

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Q: Find the given vector. Vector v of length 4 in the direction of = (-4, -4)

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Q: Find the vector v with the given length and the same direction as u. ||v|| = 3, u = (1, 0, 1, –4)

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