Which of the following statements are true? I. a=2i+6j-4k and b=-3i-9j+6k are orthogonal vectors. II. a=i-j+2k and b=2i-j+k are parallel vectors III. a=-i+2j+5k and b= 3i+4j-k are orthogonal vectors. IV. a=-3i+9j+6k and b=4i-12 j-8k are parallel vectors. O a. II, IV O b. II, IV O c. I,I d. I, III O e. I, IV

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

A: We will calculate the dot product and the angle  between these vectors to solve this question.

Q: Which of the following statements are true? I. a=2i+6j-4k and b=-3i-9j+6k are orthogonal vectors.…

A:

Q: True or false: Given two nonzero vectors v and w, v can be decomposed into two vectors, one parallel…

A: Given: Two nonzero vectors v and w, v can be decomposed into two vectors, one parallel to w and the…

Q: Which of the following vectors is parallel to the vector v = -2i +j- 2k O -4i + 2j + 4k O 4i – 2j +…

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Q: Determine if the two vectors are parallel, orthogonal, or neither. Show your proof a) A = and B =…

A: We have to determine that the given vectors are parallel , orthogonal , or neither.          (a) A→…

Q: Which of the following vectors is in the same direction as the vector a = 5i - 4j + 3k? Select one:…

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Q: For the vectors A = Ux + 3uy + 5uz , B = 2ux, 4uy + 6uz, and C = 3ux + 4uy + 5uz. Show that A x (B x…

A: For the vectors A = Ux + 3uy + 5uz , B = 2ux, 4uy + 6uz, and C = 3ux + 4uy + 5uz. To show :-A x (B x…

Q: The vector result of (ì − 2j +3k) · (−2ī + 2j − 2k) is a. -i + 7j b. -i+j-k d. j+7k e. -i+7k c.…

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Q: 3) Let å = 2ỉ +j,b = 5ỉ – 4j and c = i+j are vectors in 2D, then simplify å + b + 3č

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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: Describe all unit vectors orthogonal to both of the given vectors. −4i + 6j − 2k,   5i + 4j + 9k

A: Concept: The cross product a x b is orthogonal to both the vectors a and ba = −4i + 6j − 2kb = 5i +…

Q: Which of the following statements are false? I. a=2i+6j-4k and b=-3i-9j+6k are orthogonal vectors.…

A: We have given the following statements, I. a=2i+6j-4k and b=-3i-9j+6k are orthogonal Vectors. II…

Q: 27. Given the vectors a and b, where a = 21 – 2j + 2k and b = 3i – j + 2k are coplanar vectors, a x…

A: Given vectors are a=2i-2j+2k and b=3i-j+2k are coplanar vectors. To find: a×b Solution: We have…

Q: Vhich of the following statements are true? a=2i+6j-4k and b=-3i-9j+6k are orthogonal vectors.…

A: From given statement

Q: a) Show that the three vectors A = 2i – j+ k , B = i - 3j – 5k, Č =-3î + 4j + 4k %3D form the sides…

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

Q: 5.) Write the vector u=i+3j as the sum of two orthogonal vectors, one of which is in the direction…

A: Given vectors are: u=i+3jv=2i+5j

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: Let u= -10i+4j- 4k, v= 5i-2j+2k, w=2j-5k. Which vectors, if any are (a) perpendicular? (b) Parallel?

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Q: True or false: Given two nonzero vectors v and w, v can be decomposed into two vectors, one parallel…

A: Given that : The statement : Given two nonzero vectors v and w, v can be decomposed into two…

Q: 16. A vector perpendicular to both 21 + 21 - k and -î + 2k is: A. 31 + 4j – 2k B. 31 – 4j – 2k C. 2î…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: determine whether the vector pairs are parallel, orthogonal, or neither.  4i-9 and 18i + 8j  3i +…

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

A: The vectors 5mi^+3j^ & 2i^+7j^

Q: Given vectors u = 1.3i + 4.8lj and v = -7.4i + 2j, u and v are: Parallel vectors. O None of these.…

A: Given vectors are u=1.31i+4.81j and v=-7.4i+2jTo check if the vectors are parallel they should…

Q: In the accompanying figure, it looks as if v1 + v2 and v1 - v2 are orthogonal. Is this mere…

A: Given figure shown below.

Q: Determine whether the following vectors are orthogonal, parallel or neither. a) u = 5i – 2j + 3k and…

A: Here we have to determine the given vectors are orthogonal, Parallel, and neither. We have, a)…

Q: If the triple scalar product of the vectors A = i+ 3j + k, B = 2i -j-k and C= ai + 7j + 3k is zero ,…

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Q: Let a, b, c and y be the three dimensional vectors à = 3j+4k, b=i+6j+2k, č=4i-8j, ÿ=−i+ Perform the…

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Q: 22. Given that the vectors a = 3i-4j-4k, b = 2i-j + 3k, and c = 4i-3j +5k. The %3D %3D projection…

A: Here let d= a+b d= a + b⇒d = 5 i -5j -kProjection length of vector d = (a+b) on c is given by |d|…

Q: 16. Consider this regular octagon. If AB =d and BC =v, express each %3D vector in terms of u and v.…

A: Considering OD on x-axis. Angle at center O made by any side of regular octagon is 45degrees.

Q: 2) Let u=5i-j+k, v=j-5k and w=-15i +3j-3k. Which vectors, if any, are: a. Perpendicular? b.…

A: To find out the vectors which are parallel and perpendicular.

Q: Determine whether the vectors a = 2i-3j+ 5k, b 3i+j-2k and c=i-7j+12k are linearly dependent or…

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

Q: Consider the vectors a= 2i +4j-6k, b*=-31 +k and c = 3j¯- 2k. Find a un vector parallel to - 2a…

A: Given query is to find the indicated unit vector.

Q: Which of the following statements are false? 1. a=2i+6j-4k and b=-3i-9j+6k are orthogonal vectors.…

A: H

Q: Find the vector product (a*b) of the * two given vectors a= 2i+3j+4k, b=3i+5j, here i,j&k are unit…

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Q: Q3 - A//Find the value of M such that the vectors A 2i+ Mj+k and B = 4i-2j-2k %3D are perpendicular…

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Q: 3. Which of the following statements is correct concerning the vectors in the diagram? (а) а-Ь-с (b)…

A: Note that the magnitude and direction of a vector does not change if it is translated from one place…

Q: Determine whether the vectors v1=[12 1]^T , v2=[1 O 2]^T and v3=[5 6 7]^T are orthogonal vectors Non…

A: We have to check weather the given vector are dependent or not.

Q: Find a so that the vectors v = i- aj and w = - 9i - 8j are orthogonal. (Type an integer or a…

A: As we know that; If two vectors v & w are orthogonal to each other then the dot product or…

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: determine whether the vector pairs are parallel, orthogonal, or neither.  4i-9j and 18i + 8j  3i +…

A: to determine whether the vector pairs are parallel, orthogonal, or neither.  4i-9j and 18i + 8j  3i…

Q: Q2/ A- If this vectors are perpendicular? Prove that. A-3i +j-4k B-2i- 2j + k B- Solve that

A: Two vectors are perpendicular if and only if their dot-product is equal to zero. Dot product of two…

Q: (2) Given the vectors - -- -- --- 1 V1 = V2 = V3 = and w = are there scalars a, b, and c such that…

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Q: H.W 6- Determine which of the following vectors are parallel to A = 4i +6j 1. -4i -6j

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Q: If A= (3/2) i –(½) j + k and B= i+j+2k, what is the value of A x B? Are the vectors orthogonal? O…

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Q: 11 If m = 2i + 3j + 5k & ñ = i + 2j + 2k find the projections of m parallel and perpendicular to n.…

A: If m→=2i+3j+5k & n→=i+2j+2k, then to find the projections of m→ parallel and perpendicular to…

Q: Determine "k" so that the vectors 3a- 4b and 5a+ 2k b are collinear. Justify your response.

A: Topic = Vector

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

A: Given : 3i-2j and 4i+5mj

Q: If V1 and V2 are vectors defined as V1=3i+3j-3k and V2=2i+j+3k, then: 1- determine the angle between…

A: Given V1=3i+3j-3k and V2=2i+j+3k

Q: Which pairs of vectors are parallel? Select all that apply. OA. 10i – 15k, –4i + 6k В. 3і + 4j, —12i…

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Q: ä = 27 + 6j – 4K, b = -3ï – 9j + 6K

A:

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.