The vector (0,0,0) and the vector (0,0,0,0,0) a equal. are True False

Q: (1, Find a vector orthogonal to both (3, 2, 0) and to (0, 2, -1) of the form

A: The given question is related with vector space. We have to find a vector orthogonal to both 3 , 2 ,…

Q: The component of the vector (-5, 0, –3) onto the vector (3, –4, –2).

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Q: Find a unit vector that are orthogonal to the vector (2,−3,1), (5,−2,0), and (3,0,1)

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Q: express the vector (4,5,5) as a linear combinations of vector (1,2,3) (-1,1,4) and (3,3,2)

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Q: The vectors (3,-4,1) and (5,3,3) are orthogonal. True False

A: Topic - vector

Q: Determine a vector that is orthogonal to both (1, 2, -1) and (3, 1, 0).

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Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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Q: Consider the vector v between (-5,5, –3) and (1,1, 1).

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Q: What position vector is equal to the vector from (3, 5, -2) to (0, -6, 3)?

A: We have given two vectors;  (3, 5, -2) , (0, -6, 3)

Q: Show that the vectors ⟨1, 2, 3⟩, ⟨1, 1, 0⟩, and ⟨3, 4, 3⟩ lie in the same plane

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Q: 8. Write the vector (5,6,0) as a linear combination of the vectors (-1,2,0), (3,1,2), (4,–1,0) and…

A: We have to write the vector (5, 6, 0) as a linear combination of the vectors (-1, 2, 0) , (3, 1, 2),…

Q: Find two unit vectors orthogonal to both (2, 6, 1) and (-1, 1, 0)

A: The given vectors are The unit vectors can be obtained by the formula Now, find the cross product…

Q: (c) Are the vectors = (3, 1, 2, 1), v2 = (-1,0,1,0), 03 independent? Explain why. (3,0,0,3), v4 (5,…

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Q: (1 point) Find a vector orthogonal to both (-2, 2, 0) and to (0, 2, 3) of the form

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Q: Find two unit vectors orthogonal to both u = (1, 2, – 3) and = (0, 1, 2). %3D unit vectors =

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Q: find the components of the vector PQ. P = (-}, 3, 1), Q = (4, 6, 0)

A: P=-12, 92, 1,  Q=4, 6, 0

Q: How two-dimensional vector is determined?

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Q: (1 point) Find a vector orthogonal to both (-1,5,0) and to (0,5, 5) of the form (1,

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Q: Find a unit vector that is anti-parallel to the vector (1,2,0,3).

A: A vector is a quantity that has both magnitude, as well as direction. A vector that has a magnitude…

Q: Select all vectors perpendicular to the vector (1, 3, -5) O (2, 1, 1) O (0, 5, 3) O (1, 1, 3) O (4,…

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Q: Select all vectors perpendicular to the vector (1, 3, -5). O (2, 1, 1) O (0, 5, 3) O (1,1, 3) O (4,…

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

Q: Find a vector orthogonal to both (-3, 2,0) and to (0, 2, 1) of the form (1,

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Q: Express the vector v with initial point P and terminal point Q in component form. P(3, 3), Q(5, 5)

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Q: Show that the vectors (1, 1, 1), (1, 2, 3) and (3, 3, 4) are linearly independent?

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Q: Find two unit vectors orthogonal to both (3,2,1) and (–1,1,0).

A: The vectors 3,2,1 and -1,1,0

Q: The vectors [1, 0, 1], [1, 1, 1] and [1, 0, -1] are coplanar. True False

A: Using coplanarity conditions we have

Q: 9. Find a unit vector perpendicular to both [1,2,-3] and [2, -1, 4].

A: Given a=i+2j-3k b=2i-j+4k Aim : to find unit vector perpendicular to a and b

Q: The vectors (3, –4,1) and (5,3,3) are orthogonal. True False

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Q: Determine whether the vectors u = (-3,9,6) and v = parallel, (4, –12, –8) are orthogonal, or…

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Q: Find the magnitude of the projection of ⟨-3,-2⟩ onto the vector ⟨1,-2⟩

A: I have appended the formula used in the solution part of the question

Q: Express à = (3, 1, – 1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

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Q: Determine if the vectors (2, –2, 1) and (0,1, 2) are orthogonal.

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Q: Find the length of the vector.v = (2, 0, −5, 5)

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Q: Show that the vectors , and are coplanar.

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Q: Find the length of the vector x = [-2, 2, 6 ]

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Q: 4. Write the vector (1, 2, –2) as the sum of two vectors: one that is parallel to the vector (1, 1,…

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Q: Express the vector (2, –5, 3) in R³ as a lincar combination of the vectors (1.-3, 2), (2, –4, -1)…

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Q: Use vectors to determine whether the points (3,4,-1), (-1,6,9) and (5,3,4) are collinear.

A: The points (3,4,-1), (-1,6,9) and (5,3,4)

Q: A vector orthogonal to the plane through the points (-1,0,0), (0,0, –2), (2,3, 4) is О О O 6,-10, 3>…

A: Let, Given vectors are P(-1,0,0), Q(0,0,-2) and R(2,3,4). We have to find non zero vector orthogonal…

Q: Find two unit vectors orthogonal to both (2, 3, 1) and (-1, 1, 0).

A: Unit Vectors orthogonal to vectors  <2,3,1> and <-1,1,0>…

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, 0, -2), (2, 3, 4) is

A: We will solve the problem

Q: Find a vector orthogonal to both (-4,-4,0) and to (0,-4,-4) of the form (100)

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Q: Find the vector in R' from point A = (-2, –3, 8) to B = (9, –4,–3). AB = help (vectors)

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Q: Find a vector which is orthogonal to the vectors ū = (2, –2, 1) and ū = (4, 3, – 1).

A: Explanation of the answer is as follows

Q: The vectors (-3,4, -1) and (3, -4,1) are orthogonal. True False

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Q: )Find the vector in R2 from point A = (8,9) to B = (-3,5). AB = help (vectors)

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Q: The vectors (-1, 2, – 1) and (2, –4, 2) are parallel and not orthogonal. True False

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