flt) = Ualt) U, It) (t -3)2 + o uslt) sinzlt-s)

Q: Show that except in degen-erate cases, (u * v) * w lies in the plane of u and v, whereas u * (v * w)…

A: Show that except in degenerate cases, (u x v) x w lies in the plane of u and v, whereas u x (v x w)…

Q: orthogonal

A: We have   u=111    and v=2-12 are two column matrices  . We have to find the value of  k so that…

Q: 5. (6 + 15i ) 3

A: this is a problem of complex analysis.

Q: ) Given : Quad rilateral RSTV with diagonals RT and su intersecting at w Prove : mLT+mLa= m23 tm<4

A: In the quadrilateral,                  ∠VWR=∠TWS.

Q: 2. Cuven that 7, = -2 +ui, Z= -2i + 3 and E, - |-i. Gvaluate the followshng %3D 2 | 국 2

A:

Q: The projection of u onto v is given by projvu = ________.

A: The projection of u onto v is given by projvu = compvu.

Q: Prove VZEC, V2|z|>|Re z| +|Im z| + |Im z| Vze C,

A:

Q: Assume X, Y CU. Prove that (U \ X) U (U \ Y) = U \ (X n Y)

A:

Q: Find a non zero unit vecor î that is orthogonal to u1= (1,2,1) and Uz= (2,5,4) in R³.

A: The given vectors are u1=(1,2,1) and u2=(2,5,4) in R3

Q: What is u × w, assuming that w × u = 〈2, 2, 1〉?

A: Given,w×u=2,2,1 To find:u×w Solution: We know ,by property of cross product of two vectors (say,a…

Q: 8. Chords AC and DE intersect at Point R in OQ. If AR = 6, RC = 7, and DR = 3, what is RE? %3D %3D

A:

Q: Let = (0,- 2)v=(3,2) and w=(-2,1) Then the dot product u. (V w) is equal to

A:

Q: Complete the proof that mZXWY + MZRTU = 180°. R Statement Reason Given 1 VX || SU 2 ZXWY LUTW 3…

A: Topic:- geometry

Q: If X = U+v , y =U-V then Show that + 2 du? = 2) ( %3D nene Than ded uce that wok cu+ v*+ (u+v) g…

A:

Q: Verify that the conclusion of Clairaut's theorem holds, that is, u, Uxy = "yx' u = x'y8 – y? With u…

A:

Q: defined by ф Kerф %3D (1,-1] Kerø = {i,-i} Kero = {i,1} Kerф %3D (1,-1,1, -)

A: Option (d) is correct.

Q: find the length of the SPIYAIV-e'sVom 0=0 to 0=V5

A:

Q: Dyani wrote a proof to show that ZXWY ZYZX. What is her error? Since ZWXZ LZYW, LXZW LYWZ, and XW…

A:

Q: To/t Integrate Ua ko To 3. Uz kg 2. eT-1

A:

Q: 2. (– 13 + 3i)31

A:

Q: State why (u, v) is not an inner product for u = (ui, u:) and v = (v, V2) in R? %3D (u, v) = (u,v;)²…

A: We are given that u,v=u1v12+u2v22 for u=u1,u2 and v=v1,v2 in R2. We know that an inner product must…

Q: lar, let m = 2 and n e of A and B such that

A:

Q: 3) Given: BAC= AHC=90°. %3D Prove that: B= HAC and C= HAB. %3D %3D H. C

A: We will prove the given problem.

Q: Find a non zero unit vecor û that is orthogonal to u1= (1,2,1) and Uz= (2,5,4) in R³.

A: Cross product of two vector is perpendicular to both vectors.

Q: Show that is Reciz) e -ImZ p (ii) Im(iz) = Relz). %3D

A: Solution:- we have to show that  (1)    Re(iZ) = - ImZ (2)    Im(iZ) = Re(Z) where , Z = x + iy

Q: 6. 4, efer to the Ingure, all3WCI tII C 9, B 8, 10 F A Shape 4. If BT - IG and IG 60°, %3D %3D

A: Given figure, have to find centra angles, inscribed angles , minor angles.

Q: W Given: OWXYZ with diagonals WY and XZ Prove: 21 = 22 2

A: Given: In figure  WXYZ is a rectangle with diagonals WY and XZ. To show: ∠1≅∠2

Q: be the limear troumformation T:R¬R? ([:]) = [], T(C:1) - [:]. et, ㅜ Buch that %3D et, Them ([:]) +…

A: The encircled term is  xy=y11+14x-y440 Theorem: Let v be a vector space of dimension n. Then any…

Q: Find and when (TU – V)² In(W – UV) = In(2) at the point (T, U, V, W) = (1, 1, 2, 4).

A:

Q: Prove: For allintegers aandb, if a|b then a² |b²

A:

Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y3…

A:

Q: dual of c, is isometric to l'.

A:

Q: Prove that dv du 2 – u? + v² 18

A:

Q: Which rec tor lield s are not conservative %3D O F(ay)= (3x² - 4 y 4y=-2x> r.

A: Note : As per authoring guidelines, when multiple subparts are posted, then only first three…

Q: Complete the proof that RT || UW. W Statement Reason ZSVU E 2TSV ZQSR E ZTSV ZSVU = ZQSR 4 RT UW…

A: The given query is to find the correct reason for the statement.

Q: matrisinin özdeğerleri aşağıdakilerden hangisidir? o {,-3} po {0,1} 9o {2,-글} {2, –}} d) o {2, –2}…

A:

Q: Complete the proof that AWXY AWYX. Y W Statement Reason WX WY Given ZW ZW AWXY AWYX AAS ASA CPCTC…

A: see below the answer and explanation

Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y4…

A:

Q: From Be helie angle, ZA- No ma 9=ZAt Zる 2.comp Module ma ZA= 4 Vto Z8 Lt ZA k 2-55 ZB cosp

A: Yes it is possible. Multiply and divide the numerator of right hand side of equation by ZB. Given…

Q: Consider ỹ,,y2, ÿ,ER³ and that y,+y,+y;=0. For Î=span{ ỹ,,y} and Y=span{ỹ2, y, show that Î=Ỹ.

A: Given  that  y→1, y→2, y→3∈ℝ5 and that                   y→1+ y→2+ y→3=0→. and           Y^=spany→1,…

Q: Let V, 3 V3 = Vz= -3 8. %3D 131 2- -5 does { Vi,UeiVa} span R3?

A: Given vectors, v1 = 06-2 , v2 = 0-38 and v3 = 4-1-5 These vectors will span ℝ3 if they are linearly…

Q: 1. Prove: AMQP = LI 42. In isosceles triangle BAT, AB = AT. C o1 i Also, BR = BT = AR. If AB = 12.3…

A:

Q: prove in words: If {X, Y, Z} ` A ∧ ¬A, then {Y, Z} ` ¬X ` = derivability

A: Use the deduction theorem: Deduction theorem states that, If ┌ A⊦B then ┌⊦ A→B

Q: Find a non zero unit vecor ô that is orthogonal to u= (1,2,1) and Uz= (2,5,4) in R³.

A: We have to find a non-zero vector V that is orthogonal to u1=1,2,1 and u2=2,5,4 in R3.

Q: moves along iine ield x, y, z) = z?i + + 4 s' Theorem to finc

A: The work done is the line integral o the force along the given path C, W=∫CF.dr Apply Stokes…

Q: SU SW. Complete the proof that ASTW ASXU. T. V W Statement ZW ZU SU N SW ZS ZS 4 ASTW ASXU 2.

A:

Q: Determine las primeras derivadas parciales de la función en el punto (1,2) (u, v) = z*y - 3yA O(1,2)…

A: Find the first partial derivatives of the function at the point (1,2) f(x,y) = x2y-3y4

Q: 1. If OR 1 PQ at S, mZP = 30 and PO = 12cm, find PQ. 2. If OR 1 PQ at S, mLQ = 60 and OQ = 8cm, find…

A: Given: 1. OR⊥PQ ¯ at S, m∠P=30° and PO=12 cm2.  OR⊥PQ¯ at S, m∠Q=60° and OQ=8 cm3.  OR⊥PQ¯ at S,…

Q: Suppose that A = SS−1, where  is a diagonalmatrix with diagonal elements λ1, λ2, . . . , λn. Show…

A:

Q: Find the work done by the force F=(1,3) in moving an object from A(4, 5) to B(-2, 8).

A: Explanation of the answer is as follows