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

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: Consider the vectors [2, 1,0, 2|], [3, 1,0, 1), [1,1, 0, -1] in R. Decide whether they independent.…

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

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

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Q: Express the vector (-1, 0) as a linear combination of the vectors (-1, - 1) and (-1, 1). (-1,0) =…

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Q: Show that the vectors are orthogonal.

A: Let the given vectors be v=0i+-4j,u=-7i+0j.

Q: (a) Are the vectors (1,3, 2), (2, 1,3) and (3, 2, 1) linearly independent? (b) Are the vectors (1,…

A: We have to check

Q: Let a = (10,-1,1) and b = (5,-3,-9) be vectors. How do I find what the image is asking for?

A: (A) ⇒Projb→a→=a→·b→a→⇒Projb→a→=(10, -1, 1)·(5, -3,…

Q: Determine whether the vectors a = (1,2,3),b = (1,3,1),c =(2,2,2) plane? coplanar, that is, they lie…

A: Answer and explanation is given below...

Q: Show that the column vectors (1,1,2,4), (2,-1,-5,2), (1,-1,-4,0) and (2,1,1,6) vectors in R are…

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

A: Query- Find a vector orthogonal to the plane through the points -1,0,0,0,-2,-2,2,3,4. Answer- Let…

Q: Find two vectors of norm 1, orthogonal to all the vectors u = (2, 1, 4, 0), v = (−1, −1, −2, 2), w…

A: Given data:- u=2,1,4,0v=-1,-1,-2,2w=3,2,5,4

Q: Determine whether the given vectors (1, 1,-1, 1), (1,-1, 2,-1), (3, 1, 0, 1) in R* are lincarly…

A: Given vectors are: (1, 1, -1, 1) , (1, -1, 2, -1) , (3, 1, 0, 1) We have to determine whether the…

Q: Find the magnitude of the projection of (8, – 2) onto the vector (4, 7)

A: Wr have to find the magnitude of the projection.

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: Find all vectors u such that ux(1,1,1)=(8,-5,-3).

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Q: Show that the vectors are orthogonal.

A: Given vectors are u=<u1, u2>=<4, -1>v=<v1, v2>=<2, 8>

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: Select all vectors parallel to the vector (1,-3, 5). O (2, -6, 10) 0(-1,3,6) - 15

A: here to we need to find the parallel vectorsto the given vector from the given options. the solution…

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

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

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

Q: Find a vector in the same direction as (3, –2) with length 10.

A: The vector that has the same direction as 3,-2 has the coordinates proportional to the given vector.…

Q: Describe all vectors v that are orthogonal to u

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

A: Using coplanarity conditions we have

Q: Find two vectors that are orthogonal to ⟨0, 1, 1⟩ and to each other.

A: Vector: Let the two vectors are v and w. We have to find the two vectors which are orthogonal to…

Q: Show that the column vectors (1,1,2,4),(2,-1,-5.2) (1,-1,-4,0) and (2,1,1,6) vectors in R are…

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Q: Find two unit vectors orthogonal to a=⟨1,−1,−2⟩a=⟨1,−1,−2⟩ and b=⟨2,0,−2⟩b=⟨2,0,−2⟩.

A: Given vectors are

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

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Q: orthogonal to the vectors

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

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Q: a. From the set of vectors{ (1, 2, –1). (-4, –5, –6), (4, 3, 10). (5, –3,2)}. select two pairs of…

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Q: Show that the vectors , and are coplanar.

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Q: Show that the column vectors (1,1.2,4), (2,-1,-5,2). (1,-1,-4,0and (2,1,1.6) vectors in R are…

A: We have to prove that the given Column vectors are linearly dependent in R4.

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: Find a vector n perpendicular to the plane determined by the three points A(1, -1,2), В(2, 0, — 1)…

A: Given three points ( position vectors) are; A( 1,-1, 2) , B( 2,0,-1) and C(0, 2,1)

Q: Determine whether the set of vectors Q={(-1,1,1).(-1,0,2).(1,2,3)} spans R'.

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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 a nonzero vector orthogonal to the plane through P(2, 5, 1), Q(-3, 1, – 2) and R(5, –3, –1).

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

A: This could be solve using vector concept.

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

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

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Q: Consider the vectors (2, 1,0, 2], (3, 1,0, 1], [1, 1,0, -1] in R'. Decide whether they independent.…

A: Given: Vectors in ℝ4,                              2,1,0,2, 3,1,0,1, 1,1,0,-1 To find: Whether the…

Q: Show that the vectors (1,1,0), (1,0,1), and (0,1,1) generate F3.

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Q: Identify the vectors that are orthogonal to v = (1,2, 1) but not to w = (1,0, – 1). 口(-2,2,0) (-1,…

A: u and v orthogonal if u.v=0 i.e. let u=(x1,y1,z1) and v=(x2,y2,z2) then u.v = (x1 * x2)+(y1 *…

Q: Show that the vectors are orthogonal.

A: Given : 3,6 and 4,-2

Q: Find the two unit vectors orthogonal to both a = (4, 1, 1) and b = (-1, 4, 1). %3D

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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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