If V=R\power{3}, and W\index{1} is the xy plane and  let W\index{2} is yz-plane:      W\index{1}={(x,y,0):x,y∈R}      W\index{2}={(0,y,z):y,z∈R}  then V is not the direct sum of W\index{1} and W\index{2}.

Q: 10. Find the coordinates of the point of intersection of the line L: x = -1+ 3t, y = 2 – 2t, z = 3 +…

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Q: How many paths are there from the point (0, 0) to the point (4, 5) in the plane such that each step…

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Q: x+1 y-3 Find the equation of the plane containing line =

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Q: Under what conditions on the sacalr 'a' are the  vectors (a,1,0),(1,a,1) and (0,1,a) in R\power{3}…

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Q: 3) (i) Compute the vector projection of u onto v, proj u, where V u=(3, 3) & v= (2,0). (ii) What is…

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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: Calculate the distance from point s(10, -8, 10) to the plane 2x + 2y + z = 4 O 10 O 10 의 ~m 의 29

A: Given query is to find the distance between the plane and point. The given point is S(10, -8, 10)…

Q: 2.b) Which vector is not normal at the plane defined by 2x - 4y-6z+1=0?

A: The solution is shown in step-2

Q: Which of the listed subsets of the vector space R^3 is homogeneous but not additive?

A: option bExplanation:

Q: The normal line to the surface x² + 2y² + ² = 25 at the point (1, -2, 4) is parallel to the vector O…

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Q: (5) Consider the plane defined by x+y+z+5= 0. Let (ro, Yo, zo) be an arbitrary point in R³ and let…

A: The equation of the plane is given by:.Let  be an arbitrary point in  and  be the point in the plane…

Q: Find the volume of the parallelepiped defined by the vectors u=(1,-8,2), v=(5,0,-3), w = (1,5,-3)

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Q: ) Determine whether vectors v,(1,2,1), v2 = (1,0,2) and V3 = (1,1,0) spans the vector space (R³, R ,…

A: Given vectors v1=121, v2=102 and v3=110 We have to determine whether the vectors v1, v2, v3 spans…

Q: Explain why each set of information does not define a unique plane in three-space. a) x-intercept…

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Q: The distance from (-2,-5,-6) to the yz-plane is (A) -2 (B) 2 (C) (D) -5 (E) 6

A: Use distance between two points

Q: 2. The plane goes through point A(1,–2,3) and is parallel to the lines x = 2t y = -t +1. Write plane…

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Q: 3) Find the dimension of the vectora space ganenated by the yeetons: '= (o 1 82= (2 -1 5 4) 83- (4 0…

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Q: Find ProjS(u) where S is the space spanned by v1= (1/3)(2,1,2) and v2= (1/3)(-2,2,1). Find the…

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Q: Find its length over the given interval. (Round your answer to four decimal places.)

A: Length of a plane  curve: The length of a plane curve or the arc length of a curve r(t)=f(t) i^…

Q: 03. Which of the following is a plane that is parallel to the plane 2x2y2z = -2?…

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Q: Suppose ~u and ~w are vectors in R^n . Prove that if ~u and ~w are parallel vectors in the same…

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Q: Find the equation of the planes that contains two lines given by L₁ :x=1-2t, y = 4 + t, z = t and…

A: Given that the lines are             L1: x=1-2t, y=4+t, z=t, L2: x=2-3t, y=1+4t, x=2-t. To find the…

Q: (png)→p=T b. -p→F = p а.

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Q: Find the volume of the parallelepiped defined by the vectors u=(1,-8,2), v=(5,0,-3), w = (1,5,-3)

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Q: Find an equation of the plane passing through (0,−3,1) that is orthogonal to the planes 5x+5y−4z=0…

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Q: The planes α and β in R 3 are given via equations α : x + 2y − z − 2 = 0 and β : 2x − 2y + z − 1…

A: We find required equation of plane in given form.

Q: B Gruien Vectors i = (2,1₁-4), ✓ = (-340,2) w (11213). Find onthogonal projection of u + v along…

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Q: Is the point (1, 2, 3) on the plane = (-3,4,0)+(6,4,-2)+s(1,-4,4)? Show your work

A: The answer is given below Explanation: