Suppose that two lines Re((1+i)z+2i+3) = 0 and Re(2-bi)z+5) = 0 are perpendicular. then b=.

Q: The vector z = (2 + 2i) ( -V3 + i) lies in * the

A: The vector equation is z=2+2i-13+i.

Q: Find symmetric equations for the line through (1, 3, -2) and perpendicular to both u and v, where u…

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

Q: How do you know that for all a, b, c, d: ax + bx will be orthogonal to cx? + d ?

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Q: Show that the lines L1 : x = 4 – t, y = 2t, z = 2+t and L2 : x = 1+ 4t, y = 3 – 8t, z = 5 – 4t are…

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Q: Given the points P(-3, 4) and Q(-1, 5), express the vector PQ in terms of i and j.

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Q: D. Prove i [- 2,5, 1], 7 = [2,1, – 1] and w [- 6,0, – 12] are orthogonal. %3D

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Q: ow that c=3i -2j1+k and d=2j+ 4k are orthogonal.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 5. The ends of the transverse axis are at (+8,0) and the ends of the conjugate axis are at (0. 16).

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Q: For any two nonparallel and non orthogonal vectors a and b with angle between them, it holds that…

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Q: The orthogonal projection of v = 10i on b = −3i + j is _____ .

A: To find the orthogonal projection of v = 10i on b = −3i + j .

Q: Given that A=2i+j-k, B=4i+2j+ck, find the scalar c such that: 1- A & B are orthogonal 2- A & B are…

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Q: Let the vector ü = (k,5,-1) and v=(2k,k,3) are perpendicular in R, find the value of k that related…

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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: Q2/ Show that the vector v = ai + bj is perpendicular to the line ах + by + с.

A: A line and the vector  are said to be perpendicular to each other when the product of their sloped…

Q: Show that the lines L1 : x =1– t, y = 2t, z = 4+t and L2 : x = 1+ 3t, y= 3 – 6t, z = 5 – 3t are…

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Q: The vector parallel to intersection line of the two planes 4x-y+z=2 and 2x+y-2z=3 is: O0 -3i+6j-3k…

A: Two planes are given: 4x-y+z=2 and 2x+y-2z=3

Q: Suppose vectors v, w, and z sum to the zero vector. If v = 8.2i - 3.8j and w = 4.1i + 1.3j, find z.

A: We have to solve

Q: 5. Consider two distinct points [b1 in the and plane. Explain why the solutions of the equation det…

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Q: The vectors T and N, when defined, (a) are parallel. (b) are orthogonal. (c) have a zero cross…

A: T is the tangent vector and N is the normal vector.  So they are always orthogonal to each other.

Q: 3. Prove by the analysis of orthogonal trajectory that the lines Ax + By = C and Bx – Ay = k are…

A: let slope of line Ax+By=C is m1By=-Ax+Cy=-ABx+Cso m1=-ABslope of line Bx-Ay=k is m2Ay=Bx-kso…

Q: For any two vectors ū and i, ||ū + u|| = ||ū|| +||7||-

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Q: If the vector u = 2i-3j+v3k , then the length of u is -v2 True O False

A: # we are entitled to solve one question at a time , please resubmit the other question if you wish…

Q: For the points A(1, 5, -7) and B(3, 0, 1) vector AB has coordinates

A: Given point A and B. Find vector AB.

Q: a) Prove that ||u + v|| = ||u - v|| if and only if u and v are orthogonal, (b) Draw a diagram…

A: a) Suppose u,v are orthogonal. Now…

Q: Determine whether v = 3i - 5j and w = 6i - 10j are parallel,orthogonal, or neither.

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Q: Two vectors ñ and m are said to be parallel if n-m-0

A: False

Q: 24. The value of the constant 2, for which the plane Ax – 3y + 4z = 5 and the line r = i- 2j – 3k +…

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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: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

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Q: II. Use Theorem 6.1.1 or Theorem 6.1.2 to solve the following problem: What are the equations of…

A: From the given data, Assuming the illustration in a 2D space. Let P=α,β Then, O be the origin.

Q: Under what condition for the real numbers a,b the vectors (b,-1)(2,a) are linearly related

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Q: Mark the following statement true or false:

A: Mark the following statement true or false, In ℝ3, if non zero vectors u and v are not parallel,…

Q: For two nonzero vectors u and v, if u v=0 then u and v are parallel.

A: Given that u and v are two nonzero vectors   Dot product of two nonzero vectors u.v=|u|.|v|…

Q: 2: Find the component of u = 2i+j - 3k that orthogonal to v = 3i – j, then verify your result.

A: Solution:

Q: Check whether u = 6i – 2j+k and v=-4i – 3j+9k parallel or not are

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Q: Show that the plances x + y – z = 1 perpendicular. and 2x – 3y + 4z = 5 are neither parallel nor

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Q: Q3/ Show that the vectors (2i + 3j + 6k), (3i – 6j + 2k)and (6i + 2j + 3k) Are mutually…

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Q: Q2:Prove that the line (x-1)/2=(y+1)/3=(z-2)/(4 ) is parallel to the plane x-2y+z=6 ?

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Q: Find the cross product ax b. a - (1, 1, -1), b= (6, 8, 10) Verify that it is orthogonal to both a…

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Q: Consider the points K (−1, 0, 7) and M(1, −2, 5), the vector MN = (1, 4, −3), and the line  I with…

A: We have to solve given problems:

Q: The vector E = = -a, – 4as + 3a, expressed in RCS and in terms of ø is Е 3 (-сosф + 4sinф)ax +…

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Q: The orthogonal projection of v = 10i on b = –3i + j is <

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Q: What is the symmetric equation of the line through the points (2,1,1) and (5,-1,2). O a.…

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Q: Suppose that u and v are vectors in R^7 both of length 2√2 and that the length of    u − v is also…

A: Given, u=22v=22u-v=22

Q: Determine whether v = 3i - 5j and w = 6i + 10jare parallel,orthogonal, or neither.

A: v=3i-5j  &amp;  w=6i+10j Now the dot product is, v·w=36+-510=18-50=-32≠0 Since the dot product is…

Q: 5. Find a and b so that the lines r¡(t) = (1+t, –1+ at, 1+3t) and r(t) = (3 – 3t, 2 – 4t, 1+ bt) :…

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Q: For what values of y are the vectors yi – 2j + 3y k and 6i +j+ 3y k orthogonal.

A: To find the values of y for which the vectors yi-2j+3y k and 6i+j+3y k are orthogonal.