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

Q: For what values of b are the vectors and orthogonal?

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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: Prove the property if a and b are vectors and m is a real number.0 . a = 0

A: Given: If a and b are vectors and m is a real number. To prove: 0·a = 0

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

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Q: Let A and B be vectors in R. Show that ||A|| = || B|| if and only if A+ B is orthogonal to Ã- B.

A: To solve the given orthogonality problem related to vector.

Q: Find a vector v such that v = 15 and v is in the same direction as –li + 13j

A: The solution is given as

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: Given vectors vi = |2 and v2 = 3 V1, Vị and v3 is linearly independent. find a vector v3 in R so…

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Q: Find in terms of i and j the following vectors :

A:

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

A: According to bartleby expert policy only one individual question is to be answered. Kindly repost…

Q: a) Find the value(s) of c for which the following vectors vị = ,v2 = --- 1 and v4 are linearly…

A: According to our guideline we are supposed answer only the first question if you want any particular…

Q: [:] [] Find c so that the vectors and are parallel.

A: Find c so that the vectors c4 and 25  are parallel. Let u=c4 and v= 25 be two vectors. Two vectors…

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

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Q: Determine whether the two given vectors are orthogonal, parallel, or neither. u = 9i – 6j + 3k, v =…

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Q: Determine the real value/s of c such that the following vectors are linearly independent: 4 - 2 -6 6…

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Q: Find all values of h such that the vectors {a,, az} span R?, where a1 a2

A: Given that,

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: 1. Assume the lengths of the vectors 2a – b and a + 3b , assuming a = (2,1,3) and b = (-1,2,2)

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

Q: If a, B, y are linearly independent vectors of V(R), show that a + B, B + y, Y +a are also linearly…

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Q: 7. Prove that if A and B are any vectors, then the vectors BA + |A|B and B|A- JA|B are orthogonal.

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Q: Given the points A(1,2,3,) and B(2,-2,1) Resultant, vector C, of vectors A and B (A+B) Vector AB

A: resultant vector C = A+B  = (1+2,2-2,3+1)  = (3,0,4)

Q: Determine the value(s) of ? such that the vectors [5, ?, −8 ] and [3, ?, ?] are perpendicular.

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Q: . Given two vectors = w a = a2 show that

A: Given w→ = w1w2w3a→ = a1a2a3 We know that the cross product of w→ and a→ is w→×a→ = ijkw1w2w3a1a2a3=…

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 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: Suppose that ā and b are nonzero vectors. Under what circumstances is comp;b = comp;a? Under what…

A: A vector has 2 components, magnitude and direction which is represented by cos and sin angles. A…

Q: Find three nonzero vectors a, b, and c such that a × b = a × c = 0but b = c.

A: Find nonzero vectors a, b ,c such that a×b=a×c=0 but b≠c. If two vectors are parallel then their…

Q: Prove that two vectors v = (a, b) and w = (c, d) are perpendicular if and only if ac + bd = 0

A: we have to prove that the two vectors v=a,b and w=c,d are perpendicular if and only if ac+bd=0

Q: Determine whether the vectors AB and PQ are equal to each other.

A: Solution of the problem as follows

Q: 1. Assume the lengths of the vectors 2a – b anda+ 3b , assuming a = (2,1,3) and b = (-1,2,2)

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

Q: If a and b are vectors with the same initial point and angle between them, prove that||a - b||2 =…

A: Consider the given expression as, a-b2

Q: Ql: Determine whether the following vectors are parallel, orthogonal or neither. vi = i+ 6j – 4k, V2…

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

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+…

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Q: 7 Part (b) For each vector q and r, determine if the vector is in the span of the vectors w,, W,,…

A: Given vectors are  w1=1-124w2=230-2, w3=3-516, w4=1630 q=-893-4,r= -76-87

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: determine if the following vectors are orthogonal, parallel, or neither. Find the measure of 0. u =…

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Q: 2. Given the vectors à = (a₁, a₂, a3) and b=(b₁,b₂, b3) show that a × b = -b xã.

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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: })- The vectors and are Select one: a. Linearly dependent b. Linearly independent

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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: IH A and B are any two vectors in V, prove that (A- B) x (A + B) = 2(A X B).

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Q: (b) Find the values of s such that vectors -si – 2j+ 5sk and 9si + j+3sk are orthogonal.

A: The given vector are -si-2j+5sk and 9si+j+3sk

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

A:

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

A: Given vectors are 9i-16mj and i+4mj. To find m such that given two vectors are orthogonal. Solution:…

Q: Find the vectors T, N, and B at the given point.

A: Given vector and a point To find tangent vector T(t) use formula

Q: Resolve the vector a = -i+ 4j+9k into orthogonal vectors, one of which is parallel to b =i- 3j – k.

A: Given vectors are a→=−i^+4j^+9k^ and b→=i^−3j^−k^. Here, we using the concept of projection . We can…

Q: Under what conditions are the following true for vectors u and v in IR2 or IR3? (a) ||u + v|| =…

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.