Express the vector in the form (V= ai+ bj+ck) *, if A(1,0,3) and B is (-1,4,5):

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,−3,4) and v = (3,1,−5)

A: The cross product of two vectors is perpenducular to both of the vectors. The cross product of the…

Q: Find the area of the parallelogram that has the vectors u = ⟨3, −1, 5⟩ and v = ⟨2, −4, 1⟩ as…

A: Now

Q: Compute the angle between the vectors u = [2, 1, -2] and v = [1, 1, 1].

A: To find out the angle between two vector use the formula. First find dot product of these two…

Q: Why are there no vectors u and v in R,, such that ||u.||= 2, ||v|| = 3, and    uxv= -7?

A: The given values are, u=2, v=3,   and  u×v=-7. The objective is to find the valid reason for the…

Q: What is the resultant of vectors a and b? ( A ) GL B

A:

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: Find the vector v whose initial and terminal points are given below. (5.4, 2.4), (0.4, –2.6)

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Q: Express the vector from P(-1, -4, 6) to Q(1, 3, -6) as a position vector in terms of i, j, and k.

A: Given vectors are P-1,-4,6 and Q1,3,-6.

Q: Find a unit vector in the direction of u = (3, 4, 5).

A: Given vector, u=3, 4, 5

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, –1)

A: the given vectors are: u=-8,-6,4v=17,-18,-1 we have to find a unit vector that is orthogonal to both…

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: 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: Which two vectors are perpendicular to both a and b?

A:

Q: For the vectors u = (-1,4) and v = (-2,2), calculate proj, u and scal,u. projyu =

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

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Q: Find a unit vector that is perpendicular to both ủ = (2,1, 2) and v = (2,– 2,– 1).

A: Given, u→=2,1,2 and v→=2,-2,-1 we are asked the unit vector that is perpendicular to both.

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

A: Topic- vector calculus

Q: Find the vector v with the given length and the same direction as u.||v|| = 3, u = (0, 2, 1, −1)

A:

Q: Find the vector in R° from point A = (x, y, z) to B = (-2, –4, 1).

A: Given points  A  = (x,y,z) B = ( -2,-4,1) To determine the vector in R3 from point A to point B

Q: What is the magnitude of the vector (2, 4, –4)?

A: FORMULA

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = (3, 2, −1), v = (1, 2,…

A: Now,

Q: Find the unit vector in the same direction as the vector u = [-8, 6, 7].

A: Given,         The unit vector in the same direction as the vector u=-8,6,7.

Q: For the vectors u = (- 1,3) and v= (- 4,2), calculate proj,u and scal,,u. proj,u = ( -2,1) scalyu

A:

Q: Express A = (3, 1, – 1) as B+ C, where B is parallel to the vector (1,4, 2) and C is perpendicular…

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Q: Find the unit vector u in the di rection of the vector v=2(2, 1, 2).

A:

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

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Q: Describe all vectors v that are orthogonal to u

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Q: Express à = (3, 1, –1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

A:

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

A:

Q: vector that is orthogonal to both u and v. u  =      v  =   <15, −18,

A: Given vector u→=-8,-6,4                    v→=15,-18,-1Now , u→ x v→=i∧j∧k∧-8-6415-18-1u→ x…

Q: Compute the angle between the vectors u = [2,1, -2] and v = [1, 1,1].

A: Given: u=21-2   and   v=111 Formula Used: cosθ=u.vuv

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

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Q: Find a unit vector that is orthogonal to both u = (2, -8, 6) and v = (4, 10, -6).

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Q: Find the magnitude of the projection of (- 1, 2) onto the vector (3, 5)

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Q: What is the resultant of vectors a and b? (

A:

Q: Find a unit vector that is orthogonal to both u and v.      u = ⟨−8, −6, 4⟩,          v = ⟨10, −12,…

A: Consider the following vectors: u=-8,-6,4v=10,-12,-2 A vector orthogonal to both u and v is the…

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 unit vector u that had the same directions as the vector v= (-3,3,-2)

A: Use the basic property of unit vector

Q: For the vectors u = (-4,1) and v = (-2,3), calculate projyu and scal, u. projyu = OD

A: Here I am attaching image so that you understand each and every step.

Q: Describe a unit vector in R^3 with the same direction as &lt;1,0,7&gt;

A: Consider the given point vector

Q: Find a vector a that has the same direction as (-10,7, 10) bưut has length 4.

A: In the given problem we have to find a vector a that has the same direction as -10, 7, 10 but has…

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 unit vector that is orthogonal to both u and v. u = (-8, -6, 4) (10, -12, -2) %3D V =

A: Find the unit vector that is orthogonal to both u and v

Q: Find the vector v with the given length and the same direction as u. ||v|| = 3, u = (1, 0, 1, –4)

A:

Q: Will this statement be true or false and why? The vector u results when a vector u – v is added to…

A: topic - true