If P and Q are represented by the numbers z1 and z2 such that H- then the circumcentre of AOPQ, (where |Z, Z, 1 1 1 1 z, z, O is the origin) is (A) 2 Z, - z, (В) Z, +Z, (C) 2 +z, (D) Zi + Z2

Q: 5) If w = 4i + 4j, find 2w. 6) If v = 3i - 5j and w = -7i + 4j, find 3v - 4w. 7) If v = -4i + 4j,…

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Q: Let A=(1, 0), B=(0, 1), C=(1, 1), and D=(r, 1). Verify that R(A, B, C, D) = r.

A:

Q: Let →a=a→= and →b=b→=. Find kk so that →aa→ and →bb→ will be orthogonal (form a 90 degree angle).…

A: We Know that, Two vectors u and v are said to be orthogonal vectors if and only if u . v=0 Here, a =…

Q: Let U = N, A = {1, 3, 5}, B = {x : x² - 6x + 5 = 0}, and D = {x:x>5}. Find d. A-D e. A x B f. BxB g.…

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Q: 13. Find the intersection of [x, y, z)=[-8,-3,-5]+[1,2,-1] and [x. v.]=[1.9,4]+s[2,1,7].

A: We can find the intersection of the curve .

Q: Let a and m be real numbers, u = (1, a, 2, m, -3), and w = (2, а, 2, т, 3). Then the distance…

A: Let's find.

Q: What restrictions must be made on x, y, and z so that the triple (x, y, z) will represent points on…

A: The question asks to give restrictions must be made on x, y, and z so that the triple (x,y,z) will…

Q: Show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

A: To show that the group <a, b | a^5 = b^2 = e, ba = a^2b> is isomorphic to Z2, we need to…

Q: 1: Let u = (-3,2, 4) and v = (2, -4,6). a) Find u o (v), b) Find u x v. c) Find Proj,u.

A: Here given that                        u=(-3, 2, 4)                and  v=(2, -4, 6)

Q: Show that is isomorphic to Z2.

A:

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: Let x) 4 and gx)-x-3. Find the foilowing lock

A: To find the following expressions

Q: 1. If i = [2,-4, −1] and v = [1, −2, 4] find: a) 30-u c) Find G, where F(2, −3, 4) and FG = 3v b)…

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Q: Hiw.sLetAzi+j-2K,b=-i-k and c=zi+uj-zk,finds t Ax(B+C)- 3 CA-B)xC s-(AXB)ec 2- A (2B-c) 4-2Ax 3B 6-…

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Q: Prove that C is on the perpendicular bisector of segment AB.

A: Solution:Given A(-4,-3), B(6,1) and C (5,-11)To Prove: C is perpendicular bisector of ABi.e., to…

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: i = [4,24, 46] = r·õ+B so that i = [-4, 1,7] and B is perpendicular to

A: Introduction: The dot product of two vectors lies in the same plane as the two vectors. if two…

Q: Show that S = {x* + 1, xª + x, xª + a², xª + æ*, xª} spans PA.

A:

Q: What is the Cartesian product of A = {1, 2} and B = {a,b,c}?

A: Given A = 1, 2   and   B = a, b, c

Q: consider the relation R={(1,a),(1,b), (3,b),(3,d), (4,b)} form X={1,2,3,4} and Y={a,b,c,d}. Thus…

A: Consider the relation

Q: * vxu àu = (1,3,-3), v = (4,0,2) ......

A: Let's find.

Q: If w=f(p, q, r), where p-z2-y², q=y²-22, and r = 22-2², show that 1 Ow x 8x + 1 8w у ду + 18w z Əz…

A: Given w=f(p,q,r)and p=x2-y2,   q=y2-z2 and r=z2-x2

Q: U %3D {x\x € N Лх> 1},А %3D {-2, —1,0, 3, 6, 7, 9}, С %3D {6, 7, 8,9, 12,13}. Find: a) AnC b) AUC с)…

A: Since you have posted a question with multiple subparts according to guildlines I will solve first…

Q: 2x + 1 3 – 4x Consider the function y = f(x) a) find Ax + h) simplify fully Ax + h) – Ax) h b) find

A:

Q: A v xu u = (1,3,-3), v = (4,0.2) T......

A: Let's find.

Q: Show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

A: We have to show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

Q: Assume that (U)=110, n(B′)=55, n(A∩B′)=25, and n(A∩B)=27. Find n(A∪B)

A: For any two events A and B, it is known that n(A or B) = n(A)  + n(B) – n(A ∩ B).