Let ū = (3,2), v = (-2, –2), and w = (-4,3). Find the vector x that satisfies 5u – v +x = 7x + w. | In this case, x =

Q: Let v be the vector from initial point P1 = (3, -1) to terminal point P2 = (-2, 5).Write v in terms…

A: Given the points P1=3,-1 and P2=-2,5.   The vector is, v=P1P2→=-2-3,5--1=-5,6

Q: Let v be the vector from initial point P1 = (-1, 6) to terminal point P2 = (7, -5). Write v in terms…

A:

Q: If x is an n-vector, show that x + 0 = x.

A: Given, If x is an n-vector.

Q: Let v be the vector from initial point P1 = (-7, -4),to terminal point P2 = (0, -2). Write v in…

A: Vector u from (a,b) to (c,d) is (c-a,d-b) or  (c-a)i+(d-b)j

Q: Let f(x, y) = 5y² In(4x). Then Duf(1,4) in the direction of the vector (-2,-2) is

A: The explanation of answer as follows

Q: Let v be the vector from initial point P1 = (-1, 3) to terminal point P2 = (2, 7). Write v in terms…

A: Given : the two points are given as P1=-1,3 and P2=2,7 To find: a vector v from initial point P1 to…

Q: If is a covariant vector in Cartesian coordinates x',x2.

A: In this question, we have covariant tensor (x1x2,x2x1) By using the transformation cartesian to…

Q: Find vector V such that the vector has a length of 16 and makes an angle of n/3 with the x-axis.

A: Given problem:- Find vector V such that the vector has a length of 16 and makes an angle of π/3 with…

Q: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

Q: Let v = -7i - 7j-3 k and w =-3i+ 4j +6 k. Then the vector v – w can be written as

A: note : vector addition or subraction can be performed as  a⇀+b→ = (ax+bx,ay+by,az+bz) similarly for…

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 the x-component of the vector of length 3 in the direction of V = (-1,-1).

A: v=<-1,-1>=-i-j Unit vector in the direction of vector V i.e.,     v⏜=-i-j(-1)2+(-1)2 =-i-j2…

Q: Find a non-zero vector x perpendicular to the vectors 3 13 and u =| 4 -4 3

A: Let's find.

Q: Let v = ( 1, 2 ), Find a vector w with the same direction as v such that || w || = 7.

A: Let v=1,2 Then,  v=12+22=5 The unit vector in the direction of v is, v=vv=1,25=15,25

Q: Every vector of R²is linear combination of (-1, 1), (2, –2)? Justify

A:

Q: Find a vector B such that F = V × B and V · B = 0, where F %3D (x + Зу, у — 2z, х - 2z).

A:

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 vector c = 3u – v, if u = and v =.

A: Given u = 2i - 7j + 3k and             v = 0i + 4j -  k = 4j - k Now vector c = 3u - (1/2)v c = 3(2i…

Q: Let v be the vector from initial point P1 = (2, -1) to terminal point P2 = (5, -3). Write v in terms…

A: Given that v is the vector that has initial point P1 = (2, -1) to terminal point P2 = (5, -3).  we…

Q: Find a vector in the plane parallel to the line ax + by = c.

A: We know that, Slope of parallel lines are equal Given equation of line is ax + by = c Slope of this…

Q: Let v be the vector from initial point P1 = (-8, 6), to terminal point P2 = (-2, 3). Write v in…

A: Let v be the vector from initial point P1-8,6, to terminal point P2-2,3.

Q: Find the coordinates of a point P on the line and a vector v parallel to the line. x - 4 y + 7 = z +…

A:

Q: Let u = (1, 3), v = (2, 1), w = (4,−1). Find the vector x that satisfies 2u −v + x = 7x + w.

A:

Q: Let the vector be x = (5,6), determine its coordinates relative to the base B = {(1,1),(-1,2)}}

A: Introduction: When a basis is provided, one can represent a vector belonging to the precise vector…

Q: Let u¯¯¯=⟨−3,−5⟩, v¯¯¯=⟨2,−2⟩, and w¯¯¯¯=⟨2,4⟩. Find the vector x¯¯¯ that satisfies 9u−v+x=2x+w

A: Given that: u=-3, -5v=2, -2w=2, 4

Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

A:

Q: Let X=(1,-3)t be the transpose of vector (1,-3). If you rotate X by angle of π/3 what are the…

A: The transpose component is X=1, -3t

Q: Let v be the vector from initial point P1 = (-4, -4) to terminal point P2 = (6, 2). Write v in terms…

A: Given initial point P1=-4,-4 and terminal point P2=6,2. Given points can be written as: P1=-4i-4j…

Q: Use the vectors u = (2, 2), v = (-5, 1), and w = (2, -2) to find the indicated quantity. (v - u) -…

A:

Q: Let u = (2, 0), v = (-2, -4), and w = (-4, 1). Find the vector æ that satisfies 4u – v+ x = 9x + w.…

A: Solution:-

Q: If ï = (, 2), find a vector i that is perpendicular to ū.

A:

Q: Let v be the vector from initial point P1 = (-4, -4),to terminal point P2 = (6, 2). Write v in terms…

A: Initial point is P1=-4, -4 & terminal point is P2=6, 2.

Q: For which value of x do the following vectors form a linearly dependent set in R V =| x, x,

A:

Q: Determine R21, the vector from P2(5,2,–4) to P1 (3,–1,0). 2аx + Зау — 4а, —2ах — Зау + 4az 4ax + ay…

A: Consider the following vectors: P→1=3ax-ayP→2=5ax+2ay-4az…

Q: Show that the vectors v1, V2, and v3 are linearly dependent, where n- . -. 3 V2 = 5 and v3 = 6 Vi =…

A: The given vectors are v1=12, v2=34 and v3=56

Q: What is the magnitude of a vector joining two points P(x1, y1, z1) and Q(x2, y2, z2)?

A: The two points  are : P(x1, y1, z1) and Q(x2, y2, z2). As the vector is directed from point P to Q ,…

Q: Let v be the vector from initial point P1 = (-3, 0) to terminal point P2 = (-2, -2). Write v in…

A: Solution:- we have to find vector v in which  initial point P1 = (-3, 0) to terminal point P2 = (-2,…

Q: Show that the vectors (x1, Y1) and (x, 2) in V, (F) are linearly dependent if

A:

Q: Find a vector equation for the line that goes through the points (5,9,0) and (0, 11, 1). F(1) = with…

A: A ( 5,9,0) B ( 0,11,1)

Q: Give the vector equation of the line passing through P and Q.P = (1, 1, 0), Q = (1, 0, 1), R =…

A: P=(1,1,0) and Q=(1,0,1)we have to find vector equation of the line passing through these points

Q: What is the dependence on the following vectors: u=(3.0.1), v=(1,-1,0) and w=(1.0.1) thanks!

A: A set of vectors {v1,v2,...,vn} in Rn is said to be linearlyindependent if the vector equationx1v1 +…

Q: Let v be the vector from initial point P1 = (-1, 7),to terminal point P2 = (-7, -7). Write v in…

A: Given: Initial point P1=-1,7 Terminal point P2=-7,-7

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

A:

Q: Let v be the vector from initial point P, to terminal point P,. Write v in terms of i and j. P1 =…

A: