In the same sets of axis express the following vectors a = i+j, b = -i+j,c = a + b, d = 2a and e = a – b 1.1

Q: One of the following vectors lies in span{ 2+x + x?, 3+x- 2x2} (A) 4+ x – 7r² (B) 4+ x – 4x? (C) 4 +…

A: Solve the following

Q: Suppose that i and v are vectors in R". If ū · ū = 4 and ||v|| = 9, then || 18

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Q: Given the points P(-3, 4) and Q(-1, 5), express the vector PQ in terms of i and j.

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Q: Consider the vectors v, = (1 0) and v, = (0 1) in R,. the vector ( 0.4 3.7) can be written as a…

A: Linear combination

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

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Q: a vectors p = (2) and t = (,).

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Q: are the following vectors paralell, orthoganal or neither (explain your answer for each).   a)…

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

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Q: Given that a = (1,1) and b = (-1,0). Find a vector in the same direction as but a+b five times as…

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Q: When analyzing the vector To the sum of two vectors, the first is parallel to the vector A = 2i-i+3k…

A: There is no specific formula.Please go through the solution.

Q: When analyzing the vectorĀ = 2i – j + 3k To the sum two vectors, the first is parallel to the vector…

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Q: Find the angle between the diagonals of a parallelogram constructed on the vectors a=2 i +j and b=-2…

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Q: For the three vectors a, b and C , it is found that à•bxT = 0. Which statement below is true? %3D

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Q: For what values of c are the vectors [-8, c, 4] and [c, c²,c] orthogonal?

A: For orthogonal,dot product of vectors is equal to zero.

Q: If a = 2i -j+2k and b =i+2j-2k, find two vectors c and d satisfying all the following conditions:…

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

A: Given,

Q: Assume that the vectors a, b, c, and d are defined as follows: а - (2, 3) ь - (7, 4) с- (6, -5) d -…

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Q: One of the following vectors lies in span{ 2+x + æ2, 3+-2a2} (A) 5 + 3x + 4x2 (B) 5 + 3x + 5æ? (C) 5…

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

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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 dimension of the following set of vectors: --8 Q2 v1 = ,v3 0, v4 = A 4 B 3 D1 E None

A: The given set of vectors are: v1=101 ,    v2=213 ,     v3=000  ,       v4=112

Q: latél Show that if a is perpendicular to each of the vectors and then a is perpendicular to 26 +4

A: The detail solution is given below

Q: If a and b are two non-parallel vectors and the position vectors of P, Q and R are a + 2b, 1/2a +…

A: answer

Q: 6. Given the following vectors, Draw: a) a-b b) 2c + a c) - (c-b) a X b of

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Q: Show that each pair of vectors is perpendicular.    i + j and i - j

A: Given: u=i+j ,v=i-j

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

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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: Given v=[2,-9] and w = [7,-8], what is 2w-v written as a linear combination of unit vectors?  please…

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Q: Find the angle between the given vectors to the nearest tenth of a degree.u = <2, -4>, v =…

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Q: Find the value of a so that vectors U = ai + 6j and V 5= 9i + 12j are perpen dicular.

A: Our Aim is to find the value of a so that the vectors U=ai^+6j^ and V=9i^+12j^ are perpendicular.

Q: 4. Determine the resultant of each combination of vectors. a. 25 km/h north and 81 km/h east b. 12 N…

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Q: For what values of a are the vectors (4, -2, a) and (9, a², a) orthogonal? O -6 and 6 0 O -2√3 and…

A: Equate dot product of two vectors to zero

Q: The vectors a and bare unit vectors such that a a+b and 2a +jb are perpendicular. --Determine the…

A: The given vectors a→ and b→ are unit vectors such that a→.b→=12.Given: a→+b→ and 2a→+jb→ are…

Q: For what values of t and s does the equality (- (2t + 2), 3s + t) = (2s + 4t, 7t – 4) hold true? t =…

A: see below the answer and calculation Equating both sides means the components are equal

Q: 9. Show that for any real numbers a and b the vectors u = ai and v = bj are orthogonal?

A: Topic:-  vector algebra

Q: Given the points A(-6, 4) and B(-3, 5), express | the vector AB in terms of i and j.

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Q: in the same sets of axis express the following vectors a=i+j, b=-1+j, c=a+b, d=2a,and e=a-b

A: The vectors are:-

Q: Given the three vectors A = 3ix + 2iy – İz B = 3ix - 4iy – 5iz C= ix - İy + İz Find the following:…

A: We have to find the vector

Q: The value of A for which the vectors 2i- 4j + Ak and 3i- 6j + k parallel are

A: Given the two vectors Let's say v1 and v2 v1= 2i-4j+lemdak v2= 3i-6j+k

Q: 1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 3. +-b and Aa…

A: We have to find the value of lambda by using the data given above

Q: Express the following vectors in terms of p, q and r. GF (a) (b) CF (c) OB (d) OD le) OC

A: There are two major laws used to perform vector addition. These are Triangle law of vector addition…

Q: For each of the following pairs of vectors u and v, caloulate uov and the angle e (to the neares+…

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Q: Assume that the vectors a, b, c, and d are defined as follows: a = (8,3) b = (6,5) c = (4, -1) d…

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Q: Find the addition of the vector using the component methods. 1. 9 m/s [N30°E] and 2 m/s [N 60°E].

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Q: Find the vectors that satisfy the stated conditions. 23. (a) Oppositely directed to v (3,-4) and…

A: a) The given vector is v = <3, - 4>  To find vector opposite to given vector and half in…

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: Given the following vectors, solve for the required. A 51-9)- 7k; B 6j + 3k + 21 and C = 4)- 8i AxB…

A: Explanation of the answer is as follows

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.