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

Q: B) Determine if the two vectors are orthogonal or parallel or not? A=6i + 6k and B--2i +2j+2k

A: We have to check that the two vectors A→ and B→ are orthogonal or parallel. So, we find the angle…

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

A: Please refer the attached image for complete solution.

Q: -5 and 4 4 k are orthogonal. k =

A: We know that if two vectors u & v are orthogonal to each other then the dot product or scalar of…

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: For what values of h the vectors -3.72%3D linearly independent are

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Q: a) Let a = 2i – 3j + xk and b = -3i + j + xk. Find the values of x for which vectors a and b are at…

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Q: -9 Vị V2 -2 -8 13 ? -32 Which weights should be used for b = a1vị + a2V2 to obtain the vector b = a1…

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Q: 19 Use the given vectors to find V.w and V-V V= 6i-25, w=-4i-3

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Q: 2 3 Given the following three vectors u = |10], v = -5 and w 6 : 8. -22.

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Q: / Answerr true or Satse VAngleo- I meet makes the vectors AB 6

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Q: Consider vectors, 2 u = |2, v = w = |-3 (a) Do these vectors line in a plane ? Why? Why not? Find…

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Q: b) Consider the vectors a = 3i - 2j+7 K, and b = -5i +4j-3k, find 1-a.b 2- Angle between a and b. 3-…

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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: (3) For what value(s) of a will the vectors u = 2i + 4j-5k and v= -4i-8j + ak be parallel? V ا ) وہ…

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Q: Find the value of k for which the vectors -4] -5 and -5 k are orthogonal. k =

A: Let the two vectors be- a →=-20-51        and  b→= -4-50k It is given that both the vectors are…

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: Q.6 If vectors 3i +j-k and å i - 4j + 4k are parallel, find the value of 2.

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Q: For what value or values of a will the vectors u = 2i + 4j - 5k and v = -4i - 8j + ak be parallel?

A: Given,

Q: (b) 4x Find any values of x such that the vectors 3 and are parallel X-1 to each other.

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Q: Q1: If , r₂ and r₂ are three parallel vectors of the same magnitude Prove that ₁+₂+3 is equally…

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Q: 9. Find all the vectors with the length 6 units, which a = 2į +3j- 2k andh = i - 2j + 3k .…

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

A: The vectors 5mi^+3j^ & 2i^+7j^

Q: For what values of a and b are the vectors 4= (2a-b, -1) and v (41 3a -b) equal ? write your ans…

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Q: 6. We have two vectors: a =) and b= 8 What is the resultant of -a plus b? (

A: Given:     To find: -a + b

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: Consider the vectors A =4ax+2kaytaz and B = ax+4ay-32az what value of k the two vectors A and B will…

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Q: 27 -k are parallel. 2 Q.7 Show that the vectors 4i - 6j + 9k and -6i + 9j –

A: Two vectors are parallel if they are scalar multiple of one another i.e. if a & b are two non-…

Q: Find all values of b for which the vectors (2, -4, 5) and (b2, b, 0) are orthogonal. (Enter your…

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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: B) Determine if the two vectors are orthogonal or parallel or not? A- 6i + 6k and B-2i+2j+2k

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Q: The cross product of two vectors 3i + 4j -5k and -i+j- 2k is * 3i -11j +7k O 31 +11j +7k O 31 -11j…

A: Use Cross product of vector

Q: Determine if the vectors v = 3i i, and w = 2i -6j are parallel or not. Explain.

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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: given the followinf vectors, find |u+w| u= -3i+6j w=-2i-5j a- sqrt26 b- sqrt24 c-  -sqrt24 d- 5

A: The vectors u=-3i+6j and w=-2i-5j. Then we have to find u+w.

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

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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: Q2. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

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Q: Express the vector v =-1 as a linear combination of the vectors -3 0,v2 4 and v3 -4 , if possible.…

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Q: Q2: If u = 2i +4j- 5k and v= -4i-8j+ak, (1) For what value or values of a will the vectors u and v…

A: Given: Q2. u=2i+4j-5k and v=-4i-8j+ak. To find: (1) For what values or values of a will the vector u…

Q: 4) Find all vectors vE C? such that (1 + i)v + () = () 3+ 6i

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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 n = i-j+3k, n2 = 2i +j+ 3k to the two vectors.

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Q: 1. a. If 37-2ỷ = ở and 5x - 33 = b, express the vectors and y in terms of a and b. %3D %3D

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Q: Find a so that the vectors v=i- aj and w = 7i- 10j are orthogonal. (Type an integer or a simplified…

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

A: Topic = Vector

Q: -6 --5 Let z = and y . Find the vectors v = 47, ủ =i + ÿ, and w = 47 + y. w = || ||

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Q: a-(:) We have two vectors: a = and b= What is the resultant of -a plus b? (

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Q: Find the value of k for which the vectors -5 -1 4 and -4 k are orthogonal. k =

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Q: If a = 2i – j+k and b = 2j – k, for which value of t are the vectors a + tb and a orthogonal? 6 2 -3

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Q: Let a, b, and x denote vectors in R,,. (a) Simplify 3a + (5b -2a) + 2(b - a). (b) If 5x - a = 2(a +…

A: (a) Calculation: The simplified form of 3a+5b-2a+2b-a can be obtained as,…

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.