A. Find the values of a such that vectors < 2,-4,2a > and <-4, a, 2a > are orthogonal .

Q: Find the norm of and the unit vector ū in the direction of T if 5 3 = ||7| = 5, ||

A:

Q: Given the vectors u = (-3, 1, 2), v = (1, 2, 1), and w = u + mv, determine the value of m so that…

A: The given vectors are u=-3,1,2,v=1,2,1 and w=u+mv. We have to find the value of m.

Q: b) Prove that if b e R" is any vector, then b . X +b.a.

A: I have given the proof by using only definition of convergence of sequence

Q: Let A and B be nonzero vectors. Find k e R such that A – kB is orthogonal to A + B.

A: We know if a vector P→ is orthogonal to another vector Q→ then scalar product (dot product) is zero.…

Q: Find a vector v such that ||v|| = 20 and v is in the same direction as 15i + 15j

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Q: Write the following vector as a linear combination of the unit vectors i and j. (-4,Radical 2)

A: We need to the following vector as a linear combination of the unit vectors i and j

Q: Let v, w, and a be nonzero vectors such that v · a = w · a.Is it true that v = w? Either prove this…

A: Given: v, w and a is non zero vectors, such that: v·a=w·a To prove: v=w

Q: Find ||e − 4f||, assuming that e and f are unit vectors such that ||e + f|| = √3.

A: The step-by-step solution to the given question is ..  we have ,  e+f=3..........(1) we have to find…

Q: Show which of the following are orthogonal vectors v, = 18] V2 = %3D Or = Liel Uz = 18

A: Check the dot product of given vectors are zero or not, if zero the orthogonal otherwise not

Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Determine the length of each vector.

A:

Q: 13. Show that the pair of vectors i + i and i – i is perpendicular.

A: Two vectors is said to be perpendicular if their scalar product is zero.

Q: Find a vector v such that ||v||=20 and v is in the same direction as 15i+15j.

A: The parallel vector of a vector is the scalar multiple of the vector, and if scalar is positive then…

Q: Determine m such that the two vectors are orthogonal.

A: Given : 4mi+j and 9m-25j

Q: Prove that if the vectors a,b parallel, then āxb=0. are %3|

A:

Q: Is it true that if vectors a-b and a+b are orthogonal, then |a|=|b|.

A: For orthogonal, dot product of two vector is zero

Q: Are the following vectors Linearly Independent? Show your work vų = [2 4 – 5], v2 = [7 2 – 1],v3 =…

A: Let x, y , z be three scalers. Condition for these vectors to be independent :

Q: Prove the property if a and b are vectors and m is a real number.a . b = b . a

A: Proof : let a and b are vectors and m is real number. To prove :   a . b= b . a

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

A:

Q: Prove that if vector u is orthogonal to both vectors v and w, then u is orthogonal to v + w.

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Q: Find the value for x such that the following vectors are orthogonal. 3 1 4 -2

A: The dot product of two vectors x, y in Rn is…

Q: Determine whether the following vectors are linearly independent in R2:

A:

Q: For the vectors A = ux + 3uy + 5uz, B = 2ux + 4uy + 6uz, and C = 3ux + 4uy + 5uz, show that A × ( B…

A: For the given vectors A,B,C show the given property  If A=a1ux +a2uy+a3uz and B= b1ux+b2uy+b3uz then…

Q: Find the components of the vector ī, with |u| = 7.8 and 0 = 21.3°.

A: Given: To Find:  The components of given vector  Formula Used: The components of vector v with…

Q: In Cª, find a unit vector ū that is a positive real number multiple of z = (1 – i, i, 2, 3+ 4i).

A: Introduction: For a given complex vector z=z1,z2,...,zn, its length is formulated as…

Q: Determine if the given vectors are orthogonal. a. v = 3i – 6j and w = 8i + 4j b. s = -2i – 5j and r…

A: Consider the pair of vectors  a)v=3i−6jw=8i+4j b)s=−2i−5jr=−4i+8j

Q: Prove that the vectors v= and w= are orthogonal.

A:

Q: Determine the values of the following products of base vectors: i) а, х ад. x ag. g) ar X a, 'B . ºB…

A: Given that g)aR×aZh)aθ.aZi)aZ×aθ To determine the values of the following products of base vectors:

Q: Show that the vector in B4 is orthogonal to the vectors in B1, and that the vector in B2 is…

A:

Q: Determine whether the vector v is a linear combination of the remaining vectors. v = 3

A: (1).  The given vectors are: v→=12 ,  u1→=-1   3    and    u2→=   2-3

Q: Prove that A.B + |A x B| < 2|A||B| for arbitrary vectors A, B and C.

A:

Q: What does (a b c)=0 imply with respect to the vectors: a,b,c

A: Consider the given information. The given vectors are a, b and c. Geometrically, the scalar triple…

Q: (a) Suppose that a and b are two unit vectors in R^3, and a·b=11/24. Find the norm of the vector 4a+…

A:

Q: (B) If ū and ỹ are two vectors then prove that ū can be written as a vector parallel to v plus a…

A: given that ,  u→ and v→ are two  vectors

Q: 16. Consider this regular octagon. If AB =ü and BC =v, express each vector in terms of u and v. B C…

A: 1)from the triangle law of addition  when two vectors are moving one by another then the third…

Q: Find the norm of v, and a unit vector that is oppositely directed to v. (a) v = (3, 3)

A: The given vector is v = 3, 3

Q: A. Find the values of a are orthogonal . such that vectors and

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Which of the following vectors are not linearly independent? 日L O B O A

A:

Q: Prove that |A|B + |B|A is orthogonal to |A|B – |B|A, for any vectors A and B.

A: We need to show that |A|B + |B|A is orthogonal to |A|B – |B|A, for any vectors A and B. Here, |A|…

Q: snip

A: Assume that the set 123,  41-2,  ab3 is an orthogonal. This implies that, a, b, 3·1, 2,…

Q: . Prove: If a and b are both unit vectors, then axb is a unit vector only when a and b are…

A: since you have asked multiple questions in a single request, we would be answering only the first…

Q: Linear algebra

A: From the given information:Let,

Q: Which vector is not orthogonal to ū=? a. C. b. d.

A:

Q: Consider the vectors x1 = (2, 1)T and x2 = (6, 3)T . Determine the length of each vector.

A: Given: x1=2i+j, x2=6i+3j we know that for any given vector v=ai+bj, length l of vector is given by…

Q: Determine m such that the two vectors are orthogonal.

A: Given : 3i-2j and 4i+5mj

Q: Find a nonzero column vector u such that Cu = 4u.

A:

Q: Find a vector B for which that is parallel to A =-6i +3j –2k but has the opposite direction.

A:

Q: Find all values of h such that the vectors {a,, a,, a,} span R, where a2 a3

A: