4 2. Detemine if v = and w= are orthogonal. Explain why they are orthogonal or why not. 3

Q: Are vectors (금 ) and (금, 1, 금)' orthogonal? Justify. V3

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Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

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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: orthogonal

A: We have   u=111    and v=2-12 are two column matrices  . We have to find the value of  k so that…

Q: Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope of the…

A: Given: Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope…

Q: AB is orthogonal

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Q: Show that the vector v = ai + bj is perpendicular to the line ax + by = c by establishing that the…

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Q: Find b and c so that  (9, b, c)  is orthogonal to both  (1, 2, 7)  and  (1, −2, 1).

A: To find b and c so that (9, b, c) is orthogonal to both (1, 2, 7) and (1, −2, 1).

Q: When two nonzero vectors w are called perpendicular or orthogonal?

A: Let two nonzero vectors are u and v Then the scalar product of the two vectors is given as,…

Q: Find a vector equation for the line segment that joins P(1,3,4) to Q(-2,4,6)

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Q: 14) Determine whether u and v are orthogonal, parallel, or neither for u = and V = .

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Q: What is the unit vector oppositely directed to 4?−5?−5??

A: Topic:-  vector algebra

Q: Find the best approximation to u = (3,-7, 2, 3) as a linear combination = (2,-1,-3. 1) and =…

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Q: if vector AB=i+7j-4k and B is the point (9,3,5) find A

A: Let A=ai^+bj^+ck^B=di^+ej^+fk^ be twovectors.Then AB→=d-ai^+e-bj^+l-ck^

Q: Suppose thatu and v are vectors in both of length and that the length of u-v is and the angle…

A: Let's find.

Q: 11. If ā.b = 0, why can we not necessarily conclude that the given vectors are perpendicular? (In…

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Q: 02. Approve that the area of the parallelogram spanned by the vectors a- (2, -2, 1) and c= (-8, 8,…

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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: 6- which of the vectors X-(1,2),Y =(0,1),Z =(-2,-4 ) ,W=(-2,1), U=(-6,3) are orthogonal ,in same…

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Q: Let w,x,y,z be vectors and suppose z=−4x−3yand w=−16x+4y−4z Mark the statements below that must be…

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Q: Determine whether u and v are orthogonal, parallel, or niether. u=(-4/3,5/2) v=(16,-30)

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Q: If vector A A→ has unity magnitude and makes an angle of 60 degrees with the +x axis, then the x and…

A: Solution:

Q: 2. Use a directed line segment to represent the vector. (а) и %3D (2, —4) (b) v = (2,4, –4)

A: Given that the vector a u=2,-4  b v=2,4,-4Solution a u=2,-4u=22+-42u=20  =25b v=2,4,-4v=22+42+-42v=6

Q: Sketch the vector b = <3, 4> based at P = (−2, −1).

A: Sketch the vector b=<3, 4> based at P=(−2, −1).

Q: 6 2 Show that it is vectors are lineas dependent line or independent.

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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: Show that the set as; S = {(1, 1, 1), (2, 3, 3), (0, 1, 2)} spans R^3, write the vector (4,6,7) as a…

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Q: 03, If a=(3,-1,1), for what value ofe is the vector b-(3,c,-1) perpendicular to a?

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Q: 28. Prove that if A and B are any nonzero vectors and C- BIA + JAB, then the angle between A and C…

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Q: Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w? Explain your…

A: Given that 'x' is orthogonal to 'v' and 'w' . This implies x,v=0and x,w=0

Q: Show that the vector v = ai + bj is perpendicular to the line

A: GivenVector V = ai + bj and the line ax + by + c

Q: Suppose we know that u · v = u · w. Does it follow that v = w? If it does, give a proof that is…

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Q: A set of 3 vectors in IR^4 spans IR^4. Is this true or false?

A: Given statement is, “A set of three vectors in R4 spans R4.”

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: Which of the vectors OP = (1,-1,5) and og = (2,-1,0) is not perpendicular to the line Li- - z.…

A: The equation of a line that passes through the point x0 , y0 , z0 in three dimensional space is…

Q: Show that the vector ñ = 2î – 3j is perpendicular (orthogonal) to the line 2x – 3y – 6 = 0.

A: to Show that the  given vector is perpendicular to the  given line

Q: 4. Give an example of vectors in R3 that spans R3. (show works)

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Q: 5 Given that p andr , find in column vector form: 4 p-r ep-2

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Q: For any vectors u, v in R', we havelu + ū|? = [u|2 + [ū]2 True False

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Q: if u=(1,0,0) and v=(0,1,0), u and v are orthogonal Select one: True False

A: If dot product of two vector is zero then vectors are orthogonal

Q: The length of the vector c = (2, -3, 1) is %3D

A: Length of vector equal to magnitude of that vector  if v = <x,y,z>  then magnitude/Length =…

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: 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: Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w?

A: x is orthogonal to v and w. Then their dot product is zero. That is, ⇒x·v=0  &  x·w=0

Q: 17 jp 17 Jlgull>> حفظ الإجابت 3 درجات Two vectors ñ and m are said to be parallel if ñ m-0

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Q: Determine whether u and v are orthogonal, parallel, or neither.

A: Given vectors are u=2,18 and v=32,-16 Given vectors can be written as: u=2i+18j and v=32i-16j We…

Q: 4.15. Given vectors u = and v =, find the projection of u onto v.

A: Proceed as shown below...

Q: In Exercises 1–5, find the length and direction (when defined) of u * v and v * u. 1. u = 2i - 2j -…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 4. 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: 5. Show that if vị and vz are linearly independent vectors in R?, then any vector w E R² can be…

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