Express the vector v =-1 as a linear combination of the vectors -3 0,v2 4 and v3 -4 , if possible. Show all of the steps that you used V1 -2 11 in obtaining your solution. 3.

Q: If å = v2i +j - k, what is the vector whose alignment a is in the opposite direction and its size…

A: Given a→=2i+j−k We have to find the vector whose alignment a→ is in the opposite direction and its…

Q: Can the vector (3, −5, 2) ∈ R3 be written as a linear combination of the vectors v1 = (2, −3, 1) v2…

A: Linear Combination:Let V be a vector space and S = {v1, v2, · · · vn} ⊆ V . Then for α1, α2, · · ·…

Q: Find the angle a between the vectors  [ -5 ]    And    [ -2 ] [ 5 ]                 [ 3 ]

A: To find the angle between the vectors

Q: Express the given vector in terms of the unit vectors i, j, and k. (2, -5, 0)

A:

Q: For the pair of vectors, find U + V, U-V, and 3U - 4V U = (4,1) V =(-6,3

A: Given that  U = (4,1) V =(-6,3) To find U + V, U-V, and 3U - 4V

Q: Express the vector v = -12 -28 as a linear combination of x = 2 [² and y= -1 -6

A: We can write the answer in the below steps.

Q: given the vector, PQ, whose initial point is P(-2,-5) and whose terminal point is Q(3,4) the…

A:

Q: Consider the following 3 vectors. v1=[25−13], v2=[11−11] and v3=[−1725]. Take them pairwise, you…

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Q: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

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: Find a vector equation for the line that goes through the points (7, 6, 2) and (2, 14, 2). 7(t) =…

A: The vector equation of a line passing through any two points with position vectors a  and  b is…

Q: Find axb, a vector orthogonal to both vectors a' and b. a = (-3, 2, 1) and =(4, -2,5)

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Q: solve for th e vector x in terms of the vectors a and b. x - a= 2(x - 2a)

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Q: Find a vector perpendicular to the lines: 4₁: x = 3-4t y=-2-6t x = -1 + 2t y=4-t L₂: O O None of…

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Q: Express the vector as a product of its length and direction. 6j - 8k 100- 10(j - k) 3 10 j O 10(6j -…

A: We have to find out the vector

Q: Find the Values of for which vectors linearly dependent the are -3 4 -5 8. 6. - 2 6. -8

A: Given that three vectors are linearly dependent.

Q: Find a vector equation of the line passing through the points P(-2, 1, 3) and Q(3, 0, -2). 1+t ,te…

A: The vector equation of the line passing through the points A(x1,y1,z1) and B(x2,y2,z2)  is given by;…

Q: photo is attached

A: Given informationVector V = (-3, 5)

Q: nd the vector that has the same direction as <3, -1, 4) but has length 52.

A: First find unit vector of direction then multiply with given magnitude

Q: Write the vector (1, 2, –1) as a linear combination (if possible) as of the vectors (-1,2, 1), (2,…

A: Solution: The objective is to determine whether the given vector is linear combination of the given…

Q: Q:2) Find a vector that is parallel to the line whose equation is 5x-4 4-2z = 3 - 6y = 7 5

A: The given problem is to find the vector that is parallel to given parametric line equation, we have…

Q: Find the components of the vector ī, with |u| = 7.8 and 0 = 21.3°.

A: Given: To Find:  The components of given vector  Formula Used: The components of vector v with…

Q: Find the sum of the given vectors. а - (5, -1), ь - (-1, 8) a +b = 4,7 Illustrate geometrically. y

A: We have

Q: Find the sum of the given vectors; + B Å = 440 N Z 236°, B= 580 N Z 162° Draw and label a diagram…

A: Obtain the graph of vectors as follows: The third arrow is the resultant vector.

Q: Solve for the vector x in terms of the vectors a and b. x - a = 2(x - 2a)

A: Given: x-a=2x-2a

Q: = Find the vector equation for the line passing through the points P₁ P₂ = (2,7-13). (5,-1,-5) and

A: The given points are;  P1=(5,-1,-5) and P2=(2,7,-13).

Q: Find the equation for the plane through the point Po = (2,10,7) and normal to the vector n = 9i + 2j…

A:

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: solve for th e vector x in terms of the vectors a and b. x + 2a - b = 3(x +a) - 2(2a - b)

A:

Q: Determine if the vector is a linear combination of the remaining vectors. Explain the steps.

A: We will check whether the vector v is linear combination of others or not.

Q: ngle between the vectors -4 and 4. 2. 2.

A: We have to find the angle between given vectors.

Q: Q4) Determine if the vectors below are independent. Justify your answer. -3° - ,V2 = [2. v, = |0|…

A: Given that:      v1=002, v2=05-8, v3=-341

Q: Q1) If a vector gets multiplied by a positive number, its direction * .will be reversed

A: Given statement : If the vector gets multiplied by a positive number, it's direction will be…

Q: For the pair of vectors, find 3U- 4V. U = (3, 2), V= (-4, 3)

A: We have to find 3U - 4V

Q: Consider the vectors V1, V2, V3, and b. V1 4 V2 = 5, V3 6 ,b = 7

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Q: Find a vector equation of the line that passes through A(5,-4) and B(1,-1)

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

Q: Hi, any help on this problem would be greatly appreciated. Thank you!

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Q: Solve for the vector x in terms of the vectors a and b. x + 2a - b = 3(x + a) - 2(2a - b)

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Q: Find self-value and self-vectors.

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Q: 6. Write as a linear combination of the vectors

A: solving by linear combination of the given three vectors by converting into syatem of equation...

Q: Find the angle a between the vectors 日- 2 and a =

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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: Let a = and b = -2 be two vectors. What is Ja2|b|2 - Ja b2 ?

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Q: a a

A: For first figure. a→+a→+b→+d→-c→=02a→=-b→-d→+c→a→=-b→-d→+c→2    Answer

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 sum of the vectors - î + 23 + k and i = - î + 23 – 2k. %3D j +

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.