0. Find a basis 27 45. Consider the plane 2x1 – 3x2 + 4x3 || - B of this plane such that [] =5 [2] for i = 3 -1

Q: which of the toihts PC6,L3), Q (-5,-1,4), and R(0,3,8)15 c losest to the X2-Plane? which paint lies…

A: A point in 3D has (x,y,z) coordinates. A point on XY plane has (x,y,0) coordinates i.e. z=0 A point…

Q: a) Let a = V2+ v2 i) | Determine the minimal polynomial of a over Q. ii) | Write in terms of a…

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Q: E: Let z = 1+i and z'=i-1. 2) Are these two complex numbers independant in the complex vector space…

A: We have to check for  two complex numbers independant in the complex vector space C? For this we…

Q: 61. Find an equation for the plane consisting of all points that a equidistant from the points (1,…

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Q: 2. Carefully sketch the set of points in the complex plane defined by {z: |z−2−i| ≤ |z−1−3i|}.

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Q: Given z1=2+3i and z2=5-i. Draw on the argand plane z1,z2,z1 + z2,z1 - z2,z1,z2, z1+z2, z1 - z2

A: Given: z1=2+3i and z2=5-i Draw the following points on Argand plane: (a) z1(b) z2(c) z1+z2(d)…

Q: 1. a) Compute the point of intersection of the two lines ₁ (t) = (2+ t, 1 + 2t, 5 + 3t) and r₂(t) =…

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Q: 5. The conjugate of 2√7-√√3 is: a) √3-2√7 b)-2√7 + √3 d) 2√7 + √3 c) √7 + √3 6. In R³, the standard…

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Q: 3. Determine the intersection (if any) of the following planes. Show your work clearly ₁: 2x + 3y z…

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Q: Find the locus of the set of points z in the complex plane for which z - 4 4 Iz +6-+ t| %3D

A: Use the property z1z2=z1z2 and z=x2+y2. Take z=a+ib. So,  z-4z+6+i=4z-4z+6+i=4

Q: Prove that a finite projective plane of order n has n2 + n + 1 points and n2 + n + 1 lines.

A: Let p be an ambitrany point, each point in it determinis a line together with P which Obviously…

Q: -5 Find the orthogonal projection of v = 2 onto the plane x1 - x2+3x3 = 0 6 projection = Note: You…

A: The objective of the question is to find the orthogonal projection of a vector onto a plane. The…

Q: Let a be a real number such that a opposit to 0 . An equation of the plane passing through A…

A: Given data:- Plane passing through the points, Aa,-a,-aBa,0,2aC-a,-a,-5a

Q: v puy を basis aud anne d M orolgr oた fis (i4,d,3),(2,1;-3, -1), (0,2, 1,-5). Go Ce, -45-2,1),…

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Q: Find the symmetric equations of the L that is parallel to the two planes x+y-z= 2 and z + 3y+ z =…

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Q: Suppose P is the plane described by the equation ax+-by + cz + d = 0. Given two points (X0, Y0, Z0)…

A: Given equation of plane ax+by+cz+d=0. The plane ax+by+cz+d=0 will divide the xyz space into two…

Q: Let a = (3, −4, 9) (a) Find k such that b = (−2, k, −6) is parallel to a. (b) Find k such that b =…

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Q: Evaluate 11₁² x² zdS, where S is the part of the plane z = 3+ 4x + 2y above the rectangle S [0, 5] ×…

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Q: 4. Find the unit bivector for the plane z = x+y. Where xe₁+ ye2 + zez denotes an arbitrary point on…

A: As per the question, we are asked to determine the unit bivector for the plane defined by the…

Q: nt of intersectic -6 y + 8 = 3 O) カー

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Q: Determine and sketch the set of points in the complex plane satisfy arg(z) <and |z| ≤ 1.

A: Let, z = x + iy be any complex number satisfying            arg(z) &lt; π/4         &amp; |z| ≤ 1.…

Q: Describe the set S of all points in complex plane satisfying Re (2+ i)z +1) > 0

A: Given  inequation is                                                Re(2+i)z+1&gt;0 let…

Q: 32. a. Use definitions I and II below to prove that k[(a, b) + (c, d)] = k(a, b) + k(c, d). I.…

A: NOTE*** As per bartleby guideline for more than one question asked only first is to be answered…

Q: 7 and bɔ 3 4 Let S be the parallelogram determined by the vectors b, and let A= Compute the area of…

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Q: -7 -⠀⠀-0 Let a₁ = 4 a₂ = - 24 and b = 4 For what value(s) of h is b in the plane spanned by a, and…

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