Let P, Q, and R be the points at 1 on the x-axis, 2 on the y-axis, and 3 on the z-axis, respectively. Express QP and QR in terms of î, j, and R

Q: Let F = Vf and f = 2zy + 8xy + 6xz. Calculate F. dr for the path r₁ = (t,t,t), 0 ≤ t ≤ 1. (Give your…

A:

Q: The projection of onto the line through zero and is a. (G) b. d. 0.

A:

Q: If |r(t)| = c (a constant), then r' (t) is orthogonal to r(t) for all t.

A:

Q: Find the Ker(T) and Rng(T) and their dimensions. T:R → R defined by T(x)= Ax , where 1 -1 A = -3 3…

A:

Q: Let A = {a1, a2, a3} and D = {d1,d2, d3} be bases for V, and let P = [ [d¡]a [d2]A_ [dz]a ]. Which…

A: We will use the following theorem to find the correct option.  "Let B=b1, b2, b3,...,bn and C=c1,…

Q: Say that E = Ãek™, where the components of A and k are real and constant, i.e. they aren't imaginary…

A: A vector is a quantity that has both magnitude and direction. In general, vectors are represented as…

Q: Find the length and direction (when defined) of u x v and vxu. u= 5i + 3j – 5k, v=0

A: we know that  uxv=|u|.|v|sin∅.n^where ∅ is angle between u and v and n^ is unit vector perpendicular…

Q: Any vector in R perpendicular to -3 can be written in the form t, for some s, t eR

A:

Q: Write v as a linear combination of u and w, if possible, where u = (1, 2) and w = (1, −1). v = (−1,…

A:

Q: Given x ∈ R3, definerij =(x2i+ x2j)1/2 i, j = 1, 2, 3For each of the following, determine a…

A:

Q: Let x = 21 +mj and ỹ = -3ī +8j. Determine the value of m if: a) x and ỹ are collinear b) x and ỹ are…

A: Answer: a) x→ = 2i→+mj→ and y→ = -3i→+8j→ are colinear if m=-316 b) x→ = 2i→+mj→ and y→ = -3i→+8j→…

Q: Find the length and direction (when defined) of u x v and vxu. u= - 12i + 9j – 12k, v = - 4i + 3j –…

A: Using formula of u x v and v x u,

Q: Let v1, v2, V3 R° and suppose {v1, v2, V3 } is a linearly dependent set. Let A = [v1 v2 v3] E R5×3.…

A:

Q: graph the points z = x + iy that satisfy the givenconditions.a. | z | = 2 b. | z | < 2 c. | z |…

A: a. We have given z=2 Then, put z=x+iy This implies that x+iy=2x2+y2=2x2+y2=4 Therefore, x2+y2=4…

Q: Determine whether the following sets are linearly dependent or linearlyindependent. (a) {(; )( )} .…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Prove that if T:V-oW io a one to-one linear trans formation and 33 o a linearly deperdent then…

A:

Q: The functions y1, 2, ..., Yn are linearly independent, if and only if W (91, 32, ..., Yn)(to) #0 for…

A:

Q: m is the mid point of AB find a Of AM

A: Equating the given relation gives the value of x . Then substituting the value of x in the…

Q: Given u(x,t) =t²e¯¤, compute: Uxx

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

Q: Let v (k,2k,1) and w (k,-1,-8). For which values of k are v andw orthogonal?

A: Calculation:Since it is given that v and w are orthogonal, v ∙ w = 0.

Q: Consider the set S = {p, q, r}, where p=1+x, q= x-x² and r= 1+ 2x². Show that the set S is linearly…

A:

Q: Find all values of h such that {t² + 2,5t² + t - 7,-4t² - t + h} is a linearly dependent set in…

A: We are given a set of 3 polynomials in polynomial space P2[t] , including a unknown parameter h And…

Q: Write v as a linear combination of u and w, if possible, where u = (1, 2) and w = (1, −1). v = (1,…

A: Given u=1,2 and w=1,-1 , v=1,-4we write v is a linear combination of u and w if possible .

Q: Which of the following sets of points are not coplanar?a. E, H. O. G b. K. O. G. E c. E. O, F, J d.…

A: a) H, O, G are on a line. So if we take another point E with the line, they will be coplanar.  b) K,…

Q: Determine the real number a such that u X v| and i are orthogonal, where u = 2i + 4j + 3k and v = 8i…

A: u=2i+4j+3kv=8i-10j+αk

Q: Find f, and f, and evaluate each at the given point. f(x, y) = eXy2, (In 5, 2) fo(x, y) f,(x, v) =…

A:

Q: Determine whether the set [p., pa, p3] is linearly Independent in Pa, where pi= 3+x+3x²+4x3 Pa = 4+…

A:

Q: Let f (x, y) = x² – y² . Find all all points (æ, y) such that Vf (x, y) = ±(1, 1).

A: givenf(x, y) =x2-y2∇f(x, y) =±(1, 1)

Q: V and for all r € R. Show that (V, 1

A:

Q: Write v as a linear combination of u and w, if possible, where u = (1, 2) and w = (1, −1). v = (0,…

A: Here u = (1, 2), w = (1, -1) and v = (0, 3) Since v is a linear combination of u and w So consider v…

Q: Find the length and direction (when defined) of u xv and vxu. u= - 12i + 8j – 20k, v = - 3i + 2j -…

A: To find the length and direction of u→×v→, first find the value of u→×v→ by cross product. The given…

Q: Find the component of u along v. u = 31 - 24j, v =j

A: component of vecor u along vector v is=u→.v→v→givenu=3i-24jv=j

Q: (b) By determining constants c,, C2, C3 and c4, which are not all zero and are such that cifi(x) +…

A:

Q: Suppose Q : R? → R is a quadratic form such that Q(x) = 1 for all vectors X E R? Cuch that

A: Given: It is given that the quadratic function Q:R2→R such that Q(x)=1 for all vectors x∈R2 such…

Q: Find the Ker(T) and Rng(T) and their dimensions. T:R →R defined by T(x)= Ax, where 1 -1 27 -3 3 -6

A: The objective is to find ker(T) and range (T) and their dimension.

Q: Are the following sets linearly independent? Justify your answer. {xª, x*} 1. {In(x°), In r} 2.

A:

Q: Let r E R and --(), v- (), -- (1). 3 u = V = W = 2 For which values r ER is the set {u, v, w}…

A:

Q: For each of the given vectors x, find a Householdertransformation that zeros out the last two…

A:

Q: Show that t, e^t, and sin(t) are linearly independent.

A: In the given question we have to show that t, e^t, and sin(t) are linearly independent.

Q: Prove that Àx (Bx)= A.¿)B CA.B) wheve. A.a,t.azj+a3k. .....

A:

Q: Let r (t)= - The x component of r' (-1) =

A: r'(t)=<2t,3,5> r'(-1)=<-2,3,5>

Q: For each of the given vectors x, find a Householdertransformation that zeros out the last two…

A: Given Data The vector is x=-1,8,-4T   Let, x1=-1x2=8x3=-4   The expression for the Householder…

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, –1). v = (0, 12) a =

A: We can find the value of a and b as below.

Q: With T defined by T(x) = Ax, find a vector x whose image under T is b . 1 -3 2 6. -4 -7 -5 3

A:

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). %3D v= (0, 6) %3D b =

A: Explanation of the answer is as follows

Q: Find f and f, and evaluate each at the given point. y' f(x, y) = e*y, (In 4, 2) f,(x, y) = f,x, y) =…

A:

Q: If v1, ..., V5 are in R' and v3 = 0, then {v, V2, V3, V4, V5} is linearly dependent. %3D

A: Definition used: v1, v2, ..., vk is linearly dependent if there exist numbers α1, α2, ..., αk, not…

Q: For each of the given vectors x, find a Householdertransformation that zeros out the last two…

A: x=(3,6,2)Tx1=0 And set α=‖x‖2=7 and then set β=αα-x1=77-3=28v=x1-α,x2,x3T=(4,6,2)T

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.