Give an example of a non zero vector that is perpendicular to (5,7,4)

Q: Can the vector (3, −5, 2) ∈ R3 be written as a linear combination of the vectors v1 = (2, −3, 1) v2…

A: Linear Combination:Let V be a vector space and S = {v1, v2, · · · vn} ⊆ V . Then for α1, α2, · · ·…

Q: Find a nonzero vector parallel to the line of intersection of the two planes 2y 5x - 3x = -5 and 5y…

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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: What is the zero vector?

A: We have to define

Q: Find a vector that is orthogonal to the triangle with vertices P=(1,0,0), Q= (0,2,0), R=(1,1,1)

A: RECALL: Orthogonal vector:  Let us consider to vectors a→ and b→ then , cross product of a→ and b→…

Q: The length of the cross product between the vectors k and -k is equal to the zero vector. Select…

A: Given that , the length of the cross product between vectors k and -k is equal to the zero is it…

Q: The sum of the squares of the direction cosines of a vector in space add up to ..............

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Q: Find a vector V that is perpendicular to the plane through the points A=(0,3,4) , B=(3,-5,−5) , and…

A: Find the vector AB and vector BC. The cross product of AB→ and BC→ gives a vector which is…

Q: Express the vector (-1,5, –6) in R³as a linear combination of (2,0,7), (2,4,5) and (2, –12,13).

A: Solved below

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

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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: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

A: Given: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

Q: What is the terminal point of the vector a = (2, 2) based at P = (2,4)?

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Q: Calculate parallel component of vector a = [1,2.2] in the directoin of vector v = [7,7, 7].

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Q: Find the projection of vector A=(6,7) along vector B=(1,4).

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

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Q: are the vectors u=(-4,2) and v=(-1,2) orthogonal, parallel, or neither?

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Q: Give a vector of length 13 that is parallel to (-1,2, –2).

A: Topic- vector calculus

Q: What is the length of the vector (1, 4, 5, -3) in R^4?

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Q: how can i learnd about vector in r2 and r3?

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Q: What is the terminal point of the vector a = (4, 1) based at P = (1, 5)? Answer:

A: Use the definition of terminal point, we solve this problem as in next step.

Q: 9. Explain why four vectors is R³ are always linearly dependent.

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Q: Show that the vectors 3 do not span R° by giving a vector not in their span.

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Q: Find a non-zero vector perpendicular to

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Q: Howit Findefuation of the plane perfendicular to the vector from origin tA. through A( 2,1)_and

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Q: Find a Vector ū: non zero Vector perpendicular to the

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Q: Find a vector that is orthogonal to both v = (1, –2,3) and w = (2, 1, –1).

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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: 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 2 do not span R³ by giving a vector not in their span.

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Q: Show that the vectors do not span R' by giving a vector not in their span.

A: Solution :-

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

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Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0) Which axis on…

A: From the given points we can find two vectors and after that, using the fact that if one vector is…

Q: Project the vector b = (1,3,1)" onto the line through %3D a13D (-1,2, 2)Т, (2, 2, –1)", аz 3D az=…

A: Given: Let us assume, b= (1,3,1)T  a1=(-1,2,2)T   a2=(2,2,-1)T   a3=(2,-1,2)T

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

A:

Q: Explain how to find a vector in the direction of the line segment from P0(x0, y0, z0) to P1(x1, y1,…

A: Initial point is P0x0, y0, z0 and the terminal point is P1x1, y1, z1.

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: uppose ā and b are two non-zero vectors in R3 and they are not parallel to each other. Then, their…

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

A: False

Q: Determine whether the vectors {(1,-1,2).(-1,1,2).(0,0,1)} span R3. If they do, give the linear…

A: To discuss the linear independence (or otherwise) of the given vectors and describe their span

Q: When is a vector incomprehensible and when is a vector irrational?

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Q: Find a unit vector perpendicular to both (3,-2,4) and (-1,2,-3).

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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: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis on…

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Q: Find a vector that is perpendicular to the graph off (x, y) = 3 + 3x−y at (x, y).

A: Given: fx,y=3+3x-y The normal vector to the given graph can be determined by the gradient of the…

Q: Find the magnitude of the projection of (- 5, 6) onto the vector (– 1, 0)

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.