2 1. Let vi and H Span{v1, V2, V3}. Note that viv2 2v3 0 V2= V3 = 2 2 1 is in H. Find ul, the B-coordinate vector of u 4 c) The vector u = 6

Q: (3) Suppose a vector x is orthogonal to vectors u and v. Show that x is orthogonal to u+v.

A: We will use the fact that x is orthogonal to u and v to prove that x is orthogonal to u+v also

Q: If vector u=2i+3j+4k is orthogonal to vector v=3i+2j-bk, then value of b is 4 1 2 3

A: Two vectors x , y  are orthogonal or perpendicular if x·y=0

Q: Find the vector component of u = ⟨5, 10⟩ that is orthogonal to v = ⟨4, 3⟩, given that…

A: Given,      w1 = projvu = ⟨8, 6⟩   and     u = ⟨5, 10⟩ = w1 + w2.      Where,  u = ⟨5, 10⟩ ,  v =…

Q: Consider the vectors v, = (1 0) and v, = (0 1) in R,. the vector ( 0.4 3.7) can be written as a…

A: Linear combination

Q: 1. Let v = PQ where P = (3,4,0) and Q = (2, 3, 1) Find a vector u that is parallel to V but with a…

A:

Q: Suppose that u, v are vectors in R3 , u · v = 1, ||v|| = 1, the angle between u and v is π/3, and u…

A: The detailed solution is as follows below:

Q: a) If possible, express w as a linear combination of vectors u and v. w = - (1,0, —7), и %3D…

A:

Q: 2 7 Consider the vectors: u = 1 v = -1 w = -2 2 Express W as a linear combination au + bv. What is…

A: follow next step

Q: u.v<0, u.w < 0 ,w .u < 0 ?

A: Given data:     The given first vector is: u. The given second vector is: v. The given third vector…

Q: 2v in Given vector U= (2,5) and v = (1, –3) , determine the value of u component form.

A: Topic:- vector algebra

Q: · Let 2 be the separation vector from a fixed point (x', y', z') to the point (x, y, z), and let z…

A: Since r is the separation vector from the point x',y',z' to the point x,y,z and the difference…

Q: Let v be a vector of length 2. If w = -5v, u = (-2, –2) and the angle between w and u is . then v x…

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 vector u is a positive multiple of . Vector v = with a , what will be the signs of d, e, and f?…

A:

Q: 13. Consider the position vector i = (1,0, 0) in R³. Describe the set of position vectors v in R³…

A: Given, i=1,0,0∈ℝ3

Q: Find the magnitude of u xv and the unit vector u= 5i - 5i - 3k, v= 0 O A. 0; 5i - 5i - 3k O B. V59;…

A: Here we have, u=5i-5j-3k and v=0 We have to find the magnitude of u×v and the unit vector parallel…

Q: For what value of a is the vector v = ⟨4, -3, 7⟩ orthogonal to w = ⟨a, 8, 3⟩?

A:

Q: Let vector u= 3,4 and vector v= 6,7. Find the magnitude of 3u-4v

A: The vectors are given by u = 3,4 v = 6,7 To evaluate : The magnitude of 3u-4v

Q: +C, vnere B 1s parallel to the vector (1, 2) C is perpendicular

A:

Q: Q1. If O (0,0,0) in (x,y,z) 3-D space and r(2,5,1) draw the vector in 3D and find its direction.

A: Plot point in 3D

Q: Let A(x,y,,z) and B(x,,y2; z,) be two known 3D points. The point M on the line AB divides the vector…

A: The vectors AB, AM and MB are collinear vectors. Therefore, consider the formula for the collinear…

Q: Find the vector projy u. u = 3 i - j+ 3 k, V = 2 i+ j+ 2 k

A: We want to have projection vector. Projection of vector u on v is given by u.vvv⏞

Q: M contains the point with coordinates (0,0,1) 2 M is orthogonal to the vector 0

A: Introduction: The general equation of Plane is ax-x1+by-y1+cz-z1=0

Q: Find the vector ū which satisfies the given conditions. i =, Ju| = 2 , ū and i have opposite…

A: The unit vector,  , in the direction of the vector is calculated as follows.

Q: Dados los vectores u=2i-3j+4k y v=(4,1,-2) , calcular la norma (módulo) del vector u - 2v V37

A: Given: u=2i-3j+4k v=4,1,-2

Q: 24. Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in Figure 16, and…

A: The vectors v and w are in the x-z plane. The cross product of both vectors will yield a vector…

Q: Consider the vector v = ⟨v1, v2, v3⟩. What is the meaning of arccos v2 / II v II = 30°?

A: Consider the vector v=v1,v2,v3 Use the dot product rule: v·j=v×jcosθ=vcosθ where θ is the angle…

Q: 7 Consider the vectors: U = 1 v = w = -2 2 Express W as a linear combination au + bv. What is b'?

A: WRITE  W AS A LINEAR COMBINATION OF U AND V ie. w = au + bv Using Row Elementary Transformation,

Q: 1. For what value of c is the vector v = = (2,–5, c) orthogonal to w = (3, 2,9)?

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Show that v, = v 2 V2 3 span R and express the vector v= as a linear -7 %3D combination of v,,v2.

A: Solve the following

Q: c) Show that vector ū = 1 cannot be expressed as a linear combination of 2 in R3 3 vectors vi 1 and…

A: we have to show that , we can not write as a linear combination of vectors v1 and v2

Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: Find the length of the vector.v = (0, 1)

A: If Vector V = (V1,V2, V3) then the length of Vector ||V|| = (V1)2+(V2)2+(V3)2

Q: a. Find a unit vector perpendicular to the plane of P (4,2,1), Q (1,2,0), R (1,1,2). Whereas P is a…

A: Due to Bartleby guidelines, only 1question can be solved. Please repost the remaining questions to…

Q: Suppose that u, v are vectors in R³, u · v = 1, || = 1, the angle between u and v is T/3, and u is…

A: According to the problem, we have

Q: 1. Plot the following vectors using arrows on an xy-graph: -- (}). v-[+]. 1 u = V = 2u, u+v. Is…

A:

Q: 1. Given three vectors u =(1,–3,0), v=(2,1,–1) and w=(0,2,3). Determine: a. Bu + 4v – Sw]. b. Cosine…

A: 1. a.

Q: Find the vector W which is of length 6 and oppositely directed to u = (2,-2,1)

A: Given,          The vector w→ which is of length 6 and oppositely directed to u→=&lt;2,-2,1&gt;.

Q: Let vectors u=[1,0,-1] and v=[-2,1,2].Find the vector w that is orthogonal to both u and v

A: The given vector is u=[1,0,-1] and v=[-2,1,2]

Q: 10. Let the vector v = 2i -3j + k, and the vector w = = -i+3j+ 2k. Find v x w.

A:

Q: Find the vector of length 10 with the same direction as w = (2, V2, V3).

A:

Q: Let u, v, w be vectors and k be a scalar. Which of the followings are false? Luxv=υxu II. u. (v × w)…

A: To determine which of the statements are true, we must follow the rule of cross multiplication of…

Q: B. Find a vector has length 10 in the direction of vector V=.

A:

Q: 2 -a) Find a unit vector perpendicular to the plane that passes through the points P(1,4, 6), Q =…

A:

Q: What value(s) of a are necessary for vectors i = (2, a), and w = (4a, 3) to span R?

A:

Q: Let u = -2i + 3j, v = 6i - j, w = -3i.Find specified vector ||u + v ||2 - ||u - v||2 or scaler.

A: Given vectors are  u = -2i + 3j, v = 6i - j, w = -3i.

Q: Find a unit vector that is orthogonal to both u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩.

A: The given vectors are u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩. Compute the cross product of u and v as…

Q: Suppose that u = (0, b) is a non-zero vector in R?. Show that the line L = Span({ủ}) has Cartesian…

A: Consider the given information.

Q: 2. Determine the vector equation of the plane that contains the following two lines. L1: 7 = [ 4,…

A: