4. Let u = <-1, 3> and w = < -2, 5>. Find the resultant vector 4u + 5w.

Q: If v = 2i - 5j and w = i - j, find the vector projection of v onto w.

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Q: Find ||7e – 4f|l, assuming that e and f are unit vectors such that ||e + f|| =

A: Suppose e and f be the unit vectors such that e+f=32 First, find the dot product of the vector e…

Q: and notm ind the unit vector of V= 31 +5j -9k.

A: Given: v=3i+5j-9k To find: Unit vector of v Norm of v

Q: Find the B-coordinate vectors of ei and e2, where and B : %3D %3D %3|

A:

Q: -Let 1+t and tet? be vectors in P. write the vector plt) = S+ St+2t² as the lineor combination of P,…

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Q: Find cos(0) if 0 is the angle between the vectors u= 2i + 2j – k and v = 3i + 4k

A: Consider the two vectors. u=2i+2j-k and v=3i+4k It is given that θ is the angle between the vectors.…

Q: Given the point D(−4, 5, 3) and A = yax + (x + z)z ay, express the D and A in: Kindly answer in…

A:

Q: Let L be the line y = 6 – 4x in R?. Find vectors a and b so that v = a+tb is a vector equation for…

A: Vector equation of line

Q: Consider the vector v = (x, 2) in R2. If you rotate the vector by 90-degrees counter-clockwise, then…

A:

Q: 1. Compute the following for the vectors in R3, x [1 3 21T and y [40 1T y and y x (a) (b) 2 and y2…

A: From the given information, [1 3 –2]T and [4 0 –1]T.

Q: Q2/ Show that the vector v = ai + bj is perpendicular to the line ах + by + с.

A: A line and the vector  are said to be perpendicular to each other when the product of their sloped…

Q: 1. Determine the component of the vector shown. P 180 N y 35° 0.

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Q: Let b be a vector in R" satisfying the following equation. 4 3 =Db 7. Then m- and b

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Q: Find the angle between the vectors u = /2i - 9j and v =v2i+j-2k.

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Q: In Fr let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

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Q: Let a and y 6 Find the vectors v = 5x, u = x + ÿ, and w 5a + %3D || ||

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Q: Under what conditions are the following true for vectors u and v in R2 or R3? (a) llu +vll = llull +…

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Q: Find the magnitude only for the vector from T(-2, 6, 1) to U(10, -3, -4).

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Q: For what value of t if any, is the vector 5t, 1] parallel to the vector (4, -1) ?

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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: Compute the length of the given vector. (t) = 2t + 7 and q(t) = 7t - 5, where to = 0, t₁ = 1, t₂ = 2

A: We have to find the length of the given vectors.

Q: 2. Consider the two vectors a and b, as graphed below. 2a Plot the result of a +b on the same axes.…

A:

Q: 42. Show that the unit vector ī = xỉ + yj is not parallel to ū = yi – xj for any choice of x and y.

A:

Q: Find a unit vector that has the same direction as  4i − j + 8k.

A: we have to find a unit vector that has the same direction as 4i-j+8k let the given vector be a→…

Q: 1. Describe the vector that translates DEF to D'E'F'.

A: Given,          The vector that translates DEF to D'E'F'.

Q: 1. For the vectors u = 4i – j+4k and v= -i- 2j+3k, calculate the following: а) иху b) Vxu c) ux v

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Q: If v = 2i + 4j and w = -2i + 6j, find the vector projection of v onto w.

A: Given vectors are: v = 2i + 4j w = -2i + 6j The formula for the vector projection of v onto w is…

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: If a and b are vectors with the same initial point and angle between them, prove that||a - b||2 =…

A: Consider the given expression as, a-b2

Q: Find a unit vector that is orthogonal to both i+j and i+k ?

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Q: i +j +k andi – j -k.

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

Q: et the positon vector bc (t): Gompute He curuature KCE)

A:

Q: If A is a conutant vector and R= 3xi+ 3yj+ 32K, then grad (3A -R) = ? %3D A O 3A ©9A 27 A

A: A is a constant vector  R=3xi+3yj+3zk 3AR=9Axi+9Ayj+9Azk To find grad(3AR) Let Φ=9Ax+9Ay+9Az gradΦ=i…

Q: Express the following vector as a product of its length and direction: v = 4i + 8j – 16k -

A: Given vector is v→=4i+8j−16k. We have to express the given vector as a product of its length and…

Q: If a = i+ 10j + k and b = i+ 11j+ k, find a unit vector with positive first coordinate orthogonal to…

A: Vector cross product of given two vector  is orthogonal to two given vector

Q: If r(t) = (1 + t)/²i+ (1- t)/2j+tk, t 0 then the binormal vector B is اخترأحد الخيارات

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Q: 2. Let i= and (a) Compute the length of the vector u.

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Q: -) THREE VECTORS A, B, AND C ARE RELATED AS FOLLOWS ! A AT 180°, A +C =-5+j15, 2 C = CONJU GATE OF…

A: Solution :-

Q: 16. Consider this regular octagon. If AB =ü and BC =v, express each vector in terms of u and v. B C…

A: 1)from the triangle law of addition  when two vectors are moving one by another then the third…

Q: (b) Find a vector i that is parallel to ↑ and perpendicular to L.

A: As per your demand, we solve part b) only

Q: 4. Find the vector equation for a particle if A(t) = 6ti + 12t² j+ k, V(0) = 2i + 3j, and R(0) = 4k.

A: Given that At=6ti+12t2j+k,V0=2i+3j,r0=4k.

Q: Compute the distance between the following vectors: 2 2 w = 3 v = -4 1

A: Hope it is useful

Q: H.W 9- Given that a = (1,1) and b = (-1,0). Find a vector in the same direction as but a+b %3D %3D…

A: Given: a→=1,1, b→=-1,0 To find: A vector in the same direction as but a→+b→ five times as long.

Q: 4 3 Which weights should be used for b = a, vị + a2 V2 to obtain the vector b = ? 2 a1 = Ex: 42 az =

A: Solve the following

Q: What is the magnitude of the Vector PQ. P=(1,11) and Q= (9,3)

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Q: Given that u =, and z = What is the x component of the resultant vector w = Зи + 22

A: Given: u=4,-5z=-11,-10

Q: Find the sauare of the magnitude of the vector w =u + 2v if u = (8, 2,0) and V = (-1, 1, 2) |wf =…

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Q: Given the following points, determine the vector equation defined by having point A as initial point…

A: RCS- Rectilinear Co-ordinate System CCS-Cylindrical Co-ordinate System SCS- Spherical Co-ordinate…

Q: Show that LM = 2AB.

A:

Q: O Are the three vectors: V= 4i-8j+kV= 2i+j-2k and ū;=3i-4j+12K in the Same Plane?

A: