In Exercises 85-86, let v be the vector from initial point P to terminal point P. Write v in terms of i and j. 85. P, 3 (2, -1), Р, 3 (5, —3) 86. P, — (-3, 0), Р, — (-2,-2) %3D

Q: Find a unit vector orthogonal to both u = (1, -2, 1) v =(2, 1, 0)

A:

Q: Determine a vector that is orthogonal to both (1, 2, -1) and (3, 1, 0).

A:

Q: Determine whether the vectors (4, 2, 3)T , (2, 3, 1)T , and (2,−5, 3)T are linearly dependent.

A:

Q: Find a unit vector orthogonal to both u and v. (-3, 4, –2) (-1, 1, 0) u = V = 2 2 1 3' 3' 3

A: Given two vectors u and v, then the vector that is orthogonal to both u and v is their cross…

Q: Find the unit vector u in the direction of the vectorv=(-5, 12, 0).

A: Given          v =( -5, 12, 0 )

Q: Find the projection of vector ū = -i+ 5j + 3k onto the vector i = -i +j- 3k? %3D

A:

Q: Find a unit vector orthogonal to both u and v.u = (2, −1, 3) v = (1, 0, −2)

A:

Q: Express the vector u = (1,-8,0) as linear combination of the vectors u, =(4,5,0) and u, = (7,6,0)…

A:

Q: Find the vector projection of b onto a when b = (4, 3), a = (2, –1). 7 (2. –1) 1. vector proj. - 7…

A:

Q: (a) Are the vectors (1,3, 2), (2, 1,3) and (3, 2, 1) linearly independent? (b) Are the vectors (1,…

A: We have to check

Q: If u,v and w are linearly independent vectors other than zero vector, are the vectors u, v ,…

A: No, Not Necessarily.

Q: Exercise 6. Show that the vectors uj = (1,2, 3), uz = (-1,–1,1) in R³ are perpendicular. Find a…

A:

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

A:

Q: Find a unit vector orthogonal to both u and v.u = (−4, 3, −2) v = (−1, 1, 0)

A: Given u→=(-4,3,-2)v→=(-1,1,0) unit vector orthogonal to both u and v is gruen by     u→×v→‖u→×v→‖

Q: Sui+ (v,u2)u2+ ··+ (v,uk)uk. =(v) is the closest vector to v in U and that it is the Iv - proja(v)I

A: To show, projαv is the closest vector to v in U and that it is unique such that, v-u≥v-projαv if…

Q: Exercise 5. Suppose v is a nonzero vector. Show that any vector w can be written as w = av+ u where…

A: This is a problem of vector space, vector algebra.

Q: Let v be the vector from initial point P1 = (-3, 4) to terminal point P2 = (6, 4). Write v in terms…

A:

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

A: Given vector, u=3, 4, 5

Q: Find the vector v whose initial and terminal points are given below. (5.5,2.1), (9.5, 6.1)

A: Recall: The vector v with initial point (x1,y1) and terminal point (x2,y2) is, v=x2-x1, y2-y1 We…

Q: Find axb, a vector orthogonal to both vectors a' and b. a = (-3, 2, 1) and =(4, -2,5)

A:

Q: Find a unit vector that is orthogonal to both u = (- 1, 4, – 5) and v = (0,4,–7). %3D

A:

Q: 2. Determine whether the set of the vectors {V1, V2, V3, V4} are linearly dependent or independent.…

A:

Q: Let u be the vector with initial point p( 5,1) and terminal point q ( 2,2,) express u in terms of i…

A: NOTE: Refresh your page if you can't see any equations. . the initial point is  and the terminal…

Q: Exercise 6. Show that the vectors uj = (1,2, 3), u2 = (-1, –1, 1) in R³ are perpendicular. Find a…

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: Let u be the vector with initial point 〈-2, 6〉and terminal point 〈-8, 3〉. Write u as a combination…

A: Let, x=<-2,6>=-2i+6jy=<-8,3>=-8i+3j

Q: Find the component form of the vector u initial point (3,8,8) terminal point (5,6,10)

A: Initial point of u is (3,8,8)terminal point of u is (5,6,10)

Q: Show that the vectors (1, 1, 1), (1, 2, 3) and (3, 3, 4) are linearly independent?

A:

Q: Find the vector component of the vector U orthogonal to a: и %3D (4, —1,2) and a %3D (1,3, —2).…

A:

Q: Ui=(1, 1, 1, -1) Uz=(5, 1, 1, 1) Uз-(-3, -3, 1, -3)

A:

Q: Let å = (- 5, 5, – 3) and b = (4, – 1, 0). Find a unit vector which is orthogonal to å and b and has…

A: Given query is to find the unit vector orthogonal to a and b

Q: 9. Write the vector as a linear combination of the standard unit vectors i and j. Initial Point…

A:

Q: Let u = (-3, -1, 3) and : = (3, 1, 2). Find the vector component of u orthogonal to a. a 3D

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Find a unit vector in the direction of u = (5, 3, 2).

A: Given vector is u=(5,3,2) Find a unit vector

Q: If the vector v has initial point P, what is its terminal point? v = (-7, 0, 7), P(8, 0, –8) (x, y,…

A: in 3d space, if point P(X1, Y1, Z1) is the initial point and point T(X2, Y2, Z2) is the terminal…

Q: Use vectors to determine whether the points (3,4,-1), (-1,6,9) and (5,3,4) are collinear.

A: The points (3,4,-1), (-1,6,9) and (5,3,4)

Q: What must be a if the vectors (1,-a,1,1). (-1,a+2,–2, a –1), (0,2, –1,a² +a-4) are linearly…

A: We have to solve given problem:

Q: Exercise 6 Is the set of vectors V = {i² + 2t – 1,3t + 5, -t² + t + 6} linearly dependent?

A:

Q: Express the vector H %3D p?za, + зфzaф - рф*а, at B(3, -4, 1), in CCS.

A: The given vector is H→=ρ2z aρ+ 3Φz aΦ - ρΦ2 aZ.We have to express it in the cartesian co-ordinate…

Q: Let v be the vector from initial point P1 to terminal point P2. Write in terms of I and J P1 =…

A: Finding the vector v

Q: Exercise 7 Assume that you have a set of vectors D = {ü1, ö2, ö3, ... ön} and the linear combination…

A: We have to prove given statement:

Q: 1. what is the basic concept of a vector?

A:

Q: Find a unit vector orthogonal to both u and v. u = (-4, 5, -2) v = (-1, 1, 0)

A: The vector which is orthogonal to both u and v is defined as u×vu×v. Here, u=-4,5,-2 and v=-1,1,0.…

Q: (c) Are the vectors v1 = (3,1,2, 1), i2 = (-1,0,1,0), iz = (3,0,0,3), T4 = (5, –2,0, 4) linearly…

A:

Q: 6. Find a unit vector that is orthogonal to both [0, 1, 1] and [1,0, 1].

A: We will find the unit vector orthogonal to both the vectors as following.

Q: Describe a unit vector in R^3 with the same direction as <1,0,7>

A: Consider the given point vector

Q: Select all possible vector equations for the line through the points (1,1,1) and (3,4,5). F(t) = (1,…

A: