(a) Suppose that a and b are two unit vectors in R^3, and a·b=11/24. Find the norm of the vector 4a+ 3b.

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: 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 linearly independent vectors which generate al lutions of Ax = 0.

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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: How do I show that the vectors (1, 2), (0, 1), (-3, 4) are not linearly independent?

A: To verify that the three given vectors in the plane are linearly dependent

Q: cannot be found in such a general cas explain why. In either case, justify you 2) Let a and b be two…

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Q: 2- Suppose that vector v has initial point (-4,5) and terminal point (-1,12). a- Find the component…

A: a)A position vector v→ is defined as a line extending from the initial point (x1,y1) to the final…

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: 3. Show that if a particle moves with constant speed, then the velocity and acceleration vectors are…

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Q: 2- Are the vectores [4,2,6] and [6, 3, 9] collinear? How do you know?

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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: 3. Give two nonparallel vectors that are both orthogonal to (0, 5, 0).

A: Given A = (0,5,0) Let other two vectors be of type B = (a,b,c) A.B = a.0+b.5+c.0 A.B = 5b For…

Q: It is possible for two nonzero vectors to have a dot product of 0. True False

A: Let u and v be two nonzero vectors

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

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Q: Write the scalar equation of the line given the normal vector n =[1,−1] and a point Po (-5,1)

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Q: 10) Find two vectors of norm 1 that are orthogonal to the vectors u = and

A: Consider the provided question, u=12-23 and v=2134 Let w=ABCD be such a vector,Then, w·u=0…

Q: 8. Find the scalar equation of the line passing through the point (1, 5) that has a normal vector…

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

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Q: Find the (a) component form and (b) length of the vector with initial point P(-3, 4, 1) and terminal…

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

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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: 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: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, -4,0), v = (-1,-1,2,2), and…

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Q: The terminal point of the vector v = 3i -j+ 5k with initial point (2, 5, -5) is Do not leave any…

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Q: 7. Find a vector that has the same direction as (-2,1, 2) but twice the length.

A: GIVEN DATA : Vector of direction -2, 1, 2       TO FIND : The vector of the same direction but twice…

Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y2 + 2z2 + 4x – 4z = 0.

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Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: Determine whether Hhe Lindependent. by inspection Vectors are linearly 6. -2 -3

A: A vector is given

Q: Find the angle between the vectors (-8, –7) and (-6, 4). Carry your intermediate computations to at…

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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: 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: What helps to set of vectors linearly independent?

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Q: find two unit vectors orthogonal to (5,-5,3) and (-3,5,2)

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Q: (i) Compute each Ax by dot products of the rows with the column vector: (a) 2 1 1 2 3 [10 2 1 1 2 3…

A: Since, you have asked two questions, we are attempting only the first question for now. If you want…

Q: Show thet direcion vectors of Tue Iae メ-3 レ り+ チ一て Laeメ-コ X-3 ソャ) Z-3 -2 are orthogohal

A: Direction vectors and orthogonality

Q: 3. What is the initial point of vector w if the component form is and the terminal point is (4, 1)?

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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: Suppose v is a nonzero position vector in xyz-space. How many position vectors with length 2 in…

A: Given that, v is a nonzero position vector in xyz-space.

Q: Find two vectors of norm 1 that are orthogonal to the vectors u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2)…

A: Let X=x,y,z,t be the vector that is orthogonal to u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2) and w= (3,…

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 the angle between the vectors (-5, 4) and (-3, -1). Carry your intermediate computations to at…

A: Solution:

Q: Find a vector orthogonal to both (-4,5, 0) and to (0, 5, 4) of the form (1,

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Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y² + 2z2 + 4x – 4z = 0. |

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Q: Express (-1,2,4) as linear combination of x = (-1,2,0), y = (0,-1,1) and z = (3,-4,2) in the vector…

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

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 two unit vectors orthogonal to (-1,-1,5) and (-5,-,3,3)

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Q: Find the unit vectoru in the di rection of the vectorv=3(2, 2, 1).

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Q: The normal vector of 2x + 3y - z + 5 = 0 is: O [3, -1, 5] O [2, 3, -1] [2, 3, -1, 5] O (-2, -3, 1]

A: Answer :  From question given that the Normal vector form is  ; 2x + 3y - z + 5 = 0