27 (3) (Projections) Compute the projection of -2 onto the plane spanned by the vectors 2 and

Q: Find a vector of norm 1 that is orthogonal to the three vectors ü = (2,1,-4,0), v=(-1,-1,2,2),…

A: We have to find a vector of norm 1 which is orthogonal with the vectors u, v and w. Let a, b, c, d…

Q: Find the shortest distance from point P = (1,2,-3) to the plane which passes through (2,3,-1) and…

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Q: Compute the orthogonal  projection of v = [ -3, -3 ] onto the line L through [ 2, -2 ] and the…

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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: If a vector is multiplied by a positive scalar, how is the result re-lated to the original vector?…

A: Explanation:

Q: 6. List 3 non-zero vectors in R° that are orthogonal. (You must verify that they are orthogonal.)

A: See the detailed solution below.

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

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Q: 1. Find the set of vectors orthogonal to 2 by using the theory of Null spaces. Describe this set…

A: According to our guidelines we can solve only first question  and rest can be reposted.Thank you

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: What is the scalar projection of á = (1,0, 1) onto b = (0, 3, 4)?

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Q: Show that no linearly independent set of vectors can contain the zero vector.

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Q: Determine the set of points satisfying the condition described by Iz – 2i| + |z + 4i| express in the…

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Q: 20) Find the equation for the plane in 3-space passing through the points (2,3,2), (0, -4, 3) and…

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Q: 9. Find orthogonal projection of u=(-1, 2, 5) in the direction of v=(3, 1, -2).

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Q: Find projection of vector (0, 1, 0) into the line spanned by (0, 1,0) 0(-1,0, 2) 0(-1,3, 2) O (0, 3,…

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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 a vector of length 5 that is orthogonal to both vectors ⟨4,−1,0⟩ and ⟨−3,2,−1⟩

A: The vector orthogonal to two vectors u,v is = ± (u×v)/ |u| |v| Here u =  ⟨4,−1,0⟩ , v =…

Q: Vectors are drawn from the center of a regular n-sided polygon in the plane to the vertices of the…

A: Let us consider an incomplete regular polygon of n sides and the same polygon after rotation. We…

Q: Find the value of k such that the resultant of three vectors: [1,-1,2], [3,2,1]and [0,1,k] is…

A: Given: [1,-1,2], [3,2,1] and [0,1,k] [2,-4,1]

Q: Project the first vector orthogonally into the line spanned by the second vector. 2 3 -2

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Q: Compute the orthogonal projection of = 3 onto the line L through -2 and the origin 2 proj, (v) =

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Q: 8.) Find a vectorx such that 5x-2v=2(u-5x) SOLUTION

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

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Q: What is the vector projection of X = (7, 0, – 3) on ỹ = (-1,3,3)? Answer:

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Q: Find orthogonal projection of u=(-1, 2, 5) in the direction of v=(3, 1, -2).

A: find the orthogonal projection of u=-1,2,5 in the direction of vector v=3,1,2 it is known that…

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: 7. For the vector ū = (1,2,3), compute the 1-norm, the 2-norm, and the 0-norm.

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Q: Write the equation of the plane with normal vector n passing through point Po in the scalar form ax…

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

A: I have append the formula in solution part

Q: Suppose that A, B, and C are vertices of a triangle and that a, b,and c are, respectively, the…

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Q: (7,4) by 210 4. Use matrices to rotate the vector degrees counterclockwise about the origin.

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Q: 8. Show that the cross product u x v of the vectors u = (-3, 5, -4) and v = (-3, -5, -5) is…

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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: Show that there are infinitely many vectors in R^3 with Euclidean inner product with (1,-2,4)is zero

A: Given vector is (1,-2,4) in R^3

Q: 2. Which does not exist for a line in three-space? a) vector b) parametric c) symmetric d) scalar

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Q: Find the vector v in the plane represented by the directed line segment from (4,-3) to (-2,6)

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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: Consider the set of vectors S = {u= (-1, 2, – 1), v= (2, – 5, 0), w= (1, – 3, – 1)}, then find the…

A: u=-1, 2, -1,  v=2, -5, 0  &amp;  w=1, -3, -1. Now, u·v=-12+2-5+-10=-12 u·w=-11+2-3+-1-1=-6…

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: Find orthogonal projection of v=(3, 1, -2) in the direction of u=(-1, 2, 5).

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Q: Suppose there is a collection of three or more two- dimensional vectors. Provide an argument…

A: Collection of two dimensional vectors mean those vector having i and j components.

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: Find a vector of norm 1 that is orthogonal to the three vectors u = (2,1,-4,0), =(-1,-1,2,2),…

A: The solution is given as

Q: 6. Compute the projections of [1, – 1,0, 1] on the vector [0, 1,0, 2]. |

A: Let v = [1, -1, 0, 1] and u = [0, 1, 0, 2]

Q: Prove that swapping the order of vectors in the cross product changes the sign of the output: ьха3 -…

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Q: Find a linear mapping G that maps [0, 1] × [0, 1] to the parallelogram in the xy-plane spanned the…

A: Observe that the parallelogram is spanned by the vectors. &lt;-8,9&gt; and &lt;7,2&gt;

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: What are the projections of the point (3,−2,−7)(3,−2,−7) on the coordinate planes? on the xy plane?…

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