Determine the real number \( \alpha \) u x v and î áre orthogonal, where u = 3î + ĵ – 5k and v = 4î - 2j+ ak. Answer:

Q: Assume that the vectors sint cost X2= sint - cost , and X,= sint +cost sint -cost 0. sint +cost are…

A:

Q: Given that p and r find in column vector form:

A: In this question, we find the column vector by using the given vectors.

Q: vector v is multiplied by the scalar -, the resulting vectór 4' smaller than v and in the same…

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Q: AB is orthogonal

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Q: Compute the orthogonal projection of u onto 7. Use the square root symbol 'V' where needed to give…

A: Orthogonal projection

Q: 5. Determine the number of vectors (x1,...,x„), such that each x; is either 0 or 1 and i=1

A: (x1,x2,...,xn) is a vector with xi is either 1 or 0.  Now, ∑i=1nxi ≥ k implies at least k of the…

Q: What is meant by scalar multiple?

A: Let V be a vector space over the field ℝ. Take u,v ∈V.

Q: Let u = -i + j, v = 3i - 2j, and w = -5j.Find specified scalar 5u . (3v - 4w)or vector.

A: It is given that  u = -i + j, v = 3i - 2j, and w = -5j

Q: 4メーY - 3z = -8 -x+3y - 2z =5 2x + 2y -5z =7 ニ

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Q: Hiwil show that_Viz 3i+6j_and_V=-i-zj have offosite direction.

A: We have to prove that vectors have opposite direction.

Q: Find a vector G with curlG = sin xk.

A: Let F → = d1i+d2j+d3kThen curve F → =∇xF → =ijkddxddyddzf1f2f3Let us consider G→ = g1i+g2j+g3kThen…

Q: Find all the vectors of the family (2-jx, j4, 2-j5, jx) that are of hermitian length equal to 21.

A: Let Y=2-jx,j4,2-j5,jx Length =Y=4+x2+42+4+25+x2   Y=49+2x2 49+2x2=2149+2x2=2122x2=392x=±14

Q: Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the…

A: It is given that r1(t) and r2(t) are vector valued functions in 2-space. The objective is to explain…

Q: Let u = -2i + 3j, v = 6i - j, w = -3i.Find specified vector 3u - (4v - w)or scalar.

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j.Find specified vector or scalar 6v.

A: Given vector is v = -3i +7j.

Q: Find 3 different homogeneous coordinate representations for the Cartesian point (1,-2)

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Q: 2x+ 3y-z =1 4x + y-3z = 11 3x-2y +5z = 21 | %3D

A: Solution:

Q: Let u = -i + j, v = 3i - 2j, and w = -5j.Find specified scalar 4u . (5v - 3w)or vector.

A:

Q: Let u = -i + j, v = 3i - 2j, and w = -5j.Find specified scalar proju(v + w) or vector.

A: Here given vectors as u = -i + j, v = 3i - 2j, and w = -5j. Thus  v+w=3i-2j+-5jr(say)=3i-7j

Q: Let UsX +Sinx Deter of X 0n [0,)where ļ Find . derivalire fa 2x+1 x²+7 te tn 6x+

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Q: Compute the orthogonal projection of u onto v. Use the square root symbol 'v' where needed to give…

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Q: I. Solve the problem by using Jordan canonical form Exercise 3.2.18 Use Cramer's rule to find the…

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

Q: Parametrize y = -x2 + 4 in terms of u and v %3D

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Q: 2x+ 3y-z =1 4x + y-3z = 11 3x- 2y +5z =21

A:

Q: We need to put the sign of absolute .value for every scalar or vector TRUE O FALSE O

A: THE STATEMENT IS FALSE  AS THE ABSOLUTE VALUE MEANS ONLY THE NUMERIC VALUE AND DOES NOT INCLUDE THE…

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j.Find specified vector or scalar u - v.

A: Given u=2i-5j, v=-3i+7j.

Q: 6. A student claims to have found a vector A such that (2i - 3j + 4k) x A = (4i + 3j - k). Do you…

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Q: Prove that da(x) = a(b) a(a), %3D |

A: This is a problem from Reimann Stieltzes Integral

Q: Find the scalar equation for the plane passing through the points P-(-1. 5.-1. P=(-1, 6, 5), and…

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Q: 6ij=I, V i,j from 1 to 3 where I is identity tensor matrix.

A: To determine true or false. δij=I, ∀i, j from 1 to 3 where I is identity tensor matrix

Q: Find all values of the scalar kfor which the two vectors are orthogonal.

A: Given: u=23, v=k+1k-1 Concept Used: If two vectors are orthogonal then their dot product is zero.

Q: Suppose that a parametrization for the solution set to the equation Ax = b is -2 -3 + x2 + x3 8.…

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Q: Find all values of the scalar kfor which the two vectors are orthogonal.

A: Two vectors u and v are said to be orthogonal if u·v=0. Given that, u=1-12 and v=k2k-3 We have to…

Q: Given that complex u and v,  prove that: ||u| - |v|| ≤ |u - v |

A: In the given question we have to prove that                     for two complex number u and v…

Q: Determine k so that the vectors (1,–1, k - 1), (2, k,-4) and (0, 2 +k,-8) in R linearly independent.…

A: The detailed answer and explanation is given below:-

Q: The scalar product equal (with philand phi 2 is orthonormal) lw> =i\@,> -2|@,> Ix> =3|0,>-2i|92>

A: given:  are normalized ,that is ..............................(1)

Q: Compute the order of each element in the Quaternions, Q8. Show your work.

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Q: Compute the orthogonal projection of u'onto v. Use the square root symbol 'v' where needed to give…

A: Given vectors are u→=−64−6 and v→=−23−2. We have to find the projv→u→. We know that…

Q: Show that u and v are orthogonal if and only if ||u + v||² = ||u||2 + ||v||². (Please avoid an…

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Q: Compute the orthogonal projection of u onto v. Use the square root symbol 'V where needed to give an…

A:

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j.Find specified vector or scalar 5v.

A: Given vectors are u=2i-5j, v=-3i+7j and w=-i-6j. To find: The vector or scalar 5v. Solution: When we…

Q: Compute the orthogonal projection of u onto v. Use the square root symbol ' where needed to give an…

A:

Q: Let u = -2i + 3j, v = 6i - j, w = -3i.Find specified vector 4u - (2v - w)or scalar.

A: To Determine: find 4u-2v-w Given: we have u=-2i+3j  ,v=6i-j  ,w=-3i Explanation: we have…

Q: Solve for z using cramer's rule.  2x-y-z=4 4x+y+z=2 3y+z=2

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Q: -) Are these pairs of vectors orthonormal or only orthogonal or only linearly independer [:]; » [] 1…

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Q: Find the scalar product of x and y x =(-1, 0, 2) and y =(-7, 7, 3)

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Q: Find the scalar component of 6 a, +2 a,-3 a, along 3 a,- 4 a,

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Q: 4) Show that, in general, (A.B)" = B".AT How is (A.B) related to (B.A) when both tensors A and B are…

A: 4.

Q: If specified scalar 1 2i-j, v = 3i+j₁ V Find the 4= v. (4+w) W = i + 4 j Del cksp

A: To find the required scalar obtained after performing given operations on vectors.

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.