Let U(9, 9, 2), V(9, t, 4), and W(2, 5, 8). U, V and W have the same starting point. find t for which U, V and W are coplanar (same Plane)

Q: Find a vector å with representation given by the directed line segment AB, for A(0,3,1) and B(2,3, –…

A: We have to find the vector and draw it.

Q: What should k be if the vectors x=(1,1,k) y=(1,3,1) z=(k,1,3) are in the same plane in the Euclidean…

A: Three vector a1,a2,a3,b1,b2,b3 and c1,c2,c3 will be in euclidean space ℝ3 If  a1a2a3b1b2b3c1c2c3=0…

Q: Use a graphing utility to find u × v, and then show that it is orthogonal to both u and v.u = (2, 0,…

A:

Q: Find a vector a with representation given by the directed line segment E A(0, 3, 2), B(5,3, -5) Draw…

A: We need to find the equation from A(0, 3, 2) and B(5, 3, -5).

Q: Show that a set of vectors {v,, v2. ..., V5} in Rn is linearly dependent when dim Span {v,, v2, ...,…

A: We need to show that: {v1, v2, v3, v4, v5}  in Rn are linearly dependent when  dim Span{v1, v2, v3,…

Q: (3,8, 0) is u x v = %3D So the cross product of u = (1, 0, 1) and v =

A:

Q: Prove that (i) the three points A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6) are collinear, (ii) the four…

A: (1) Given points are A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6)

Q: 11. Use vectors to show that the distance from P:(x1, yı) to the line ax + by = c is |ax, + by, – c|…

A:

Q: Let the vector ü = (k,5,-1) and v=(2k,k,3) are perpendicular in R, find the value of k that related…

A:

Q: Let u (a, b, c) and v = (4, 5, 6). If u is parallel to (1,0, –1) and the projection of u along v is…

A:

Q: Find u × v and show that it is orthogonal to both u and v.u = (−2, 1, 1), v = (4, 2, 0)

A:

Q: For what values of m and n are vectors [m,n,1], [2,1,3] and [2,1,1] coplanar?

A:

Q: Let u = (a, b, c) and v = (8,9, 10). If u is parallel to (1,0, –1) and the projection of u along v…

A:

Q: 8. Which line does not lie on the plane r = (1,5,0) + s(2,-3,1)+t(1,−1,4), s,t € R? a. V = (1,5,0) +…

A: To Find: Which of the given lines does not lie on the plane r = (1,5,0)+s(2,-3,1)+t(1,-1,4) where…

Q: Find u × v and show that it is orthogonal to both u and v.u = (2, −3, 1), v = (1, −2, 1)

A:

Q: Determine whether u and v are orthogonal, parallel, or niether. u=(-4/3,5/2) v=(16,-30)

A:

Q: If vector AB = i + 4j - 2k and B is the point (5, 1, 3), find A.

A: Given,

Q: Find a vector a with representation given by the directed line segment AB. A(-4, -2), В(2, 5) Draw…

A: A vector from point A (x1,y1), to point B (x2,y2) is given by AB =(x2-x1)I +(y2-y1)j

Q: Find a vector a with representation given by the directed line segment AB. A(5, 4), B(0, 8)

A: We have to find a vector a with representation given by the directed line segment AB.

Q: Find a vector a with representation given by the directed line segment AB, where A(−5, 0, 1) and…

A:

Q: a) Prove that ||u + v|| = ||u - v|| if and only if u and v are orthogonal, (b) Draw a diagram…

A: a) Suppose u,v are orthogonal. Now…

Q: Find u × v and show that it is orthogonal to both u and v.u = (4, 1, 0), v = (3, 2, −2)

A: Now cross product is,

Q: compute the component of u along v. u = (3, 0, 9), v = (1, 2, 2)

A: the given vectors are: u=3,0,9v=1,2,2 we have to compute the component of u along v.

Q: 8) Find the cross product a x b and verify that it is orthogonal to both a and b. a = (1, 1, -1),…

A:

Q: Find a vector å with representation given by the directed line segment AB, for A(-1, 1) and B(3, 2).…

A:

Q: Find a vector a with representation given by the directed 个 line segment AB, where A(–6, −6) and…

A:

Q: Suppose {u1,u2,...,un} is a set of vectors that span V, and that {v1,v2,...,vk} is an independent…

A:

Q: Let u = (1, 2, 3, 4), v = (0, 2, t, 3), and w = (1, 1, 0, 1). Find t so that u + v and w are…

A: Here, u=(1,2,3,4),v=(02,t,3) & w=(1,1,0,1)

Q: 11. Let a, =3 ,b3-5 For what value(s) of h is b in the plane spanned by a, and a2?

A: We have to find the value of h

Q: Let u = (k, 2 − k, −1), v = (2k, k, 3). Find k such that u and v are orthogonal.

A: Let u = (k, 2 − k, −1), v = (2k, k, 3)

Q: Use a graphing utility to find u × v, and then show that it is orthogonal to both u and v.u = (1, 2,…

A: Using the graphing utility, w = u × v = (1, 2, −1) x (2, 1, 2) = (5, -4, -3)

Q: Find all values of c so that (2, 1, c) and (c – 1, 2, 2c) orthogonal. are

A:

Q: What is the Cartesian Product of Z × X × Y, where X = {3,–1}, Y = {m, l, 0} and Z {w,b}.

A:

Q: Find the norm of U = V + 3W V(9 , 10 , 1) and W(8, -4,-9)

A: The given two vectors are V=(9, 10, 1) and W=(8, -4, -9). Evaluate U as follows. U=V+3W=9, 10, 1+38,…

Q: Use a directed line segment to represent the vector.u = (2, −4)

A:

Q: 12. Given the sct of vectors S = {(6,2,1), (4,-3, 1), (5, 8, 2)} of R, is this set linearly…

A: Given: S=6, 2, 1, 4, -3, 1, 5, 8, 2 To check: Whether the set S is linearly independent and the…

Q: if u=(1,0,0) and v=(0,1,0), u and v are orthogonal Select one: True False

A: If dot product of two vector is zero then vectors are orthogonal

Q: If u = (3, −1, 4) and v = (−2, 3, 5), the scalar projection of y onto v is:

A:

Q: 2. Show that the ry plane W = (r, y, 0) in R³ is generated by: (i)u = |2 and v= (ii)u = and v=

A: Please see the below picture for detailed solution.

Q: Verify that (u,,u2} is an orthogonal set, and then find the orthogonal projection of y onto Span…

A:

Q: When the set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2, . . . ,…

A: We have given; The set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2,…

Q: Let y→=[−8, −7] and u→=[−2, 6]. Write y→ as the sum of two orthogonal vectors, x→1 in Span{u} and…

A:

Q: Consider the set of vectors {u" ,v ,w° } in R°, where u =(4,-4,8), v =(9,6,3) and w =(-9,-21,k),…

A:

Q: Use a directed line segment to represent the vector.u = (−3, −4)

A: The directed  line segment is the vector drawn from the any two points in the cartesian plane. The…

Q: Find u × v and show that it is orthogonal to both u and v.u = (12, −3, 1), v = (−2, 5, 1)

A: Given vectors u=12,-3,1v=-2,5,1 Their cross product is u×v=ijk12-31-251…

Q: In Exercises 1–5, find the length and direction (when defined) of u * v and v * u. 1. u = 2i - 2j -…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Let

A:

Q: Let u= (2, 1, –1) v- -4,3α + β, 2) w- (α, 0, 2β) Find the values of a and B such that u is parallel…

A: Given, u=2,1,-1v=-4,3α+β,2w=α,0,2β