For Exercises 20–25, perform the indicated operations on the following vectors: ā - 27 +k, i --37 + 55 + 4k, i -7 + 67, --2ī + 97, j - 4ï – 7j, z -7 - 37 –k.

Q: Let u = 4i + 5j, v = -4i +2j, and w = 3i - j. Determine the i, j form of each of the following: (a)…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Consider the vectors: å = ỉ– 3j + 2k , b' = 4j – 2k and ở = i + k in 3D A. Write 3a – 4 b - 2¢ in a…

A:

Q: Compute (u v Ղա • Ա. . — u = (i, 7,6), v = (2, -7i, 1+i), w = (7-i, 7i, 3 + 6i) u · v) ա • Ա —

A:

Q: The projection of the vector 5î + 5ĵ – 5k onto the vector –4î + 2ĵ – 4k. | |

A: We have to find out

Q: The figure below shows four named points A, B, C, and D on a grid generated by two vectors ₁, ₂ in…

A:

Q: Evaluate ( 3+j4)( 3+j4) = A +jB, determine the real component A

A: Given,              (3+j4)(3+j4)=A+jB

Q: 6. is applied to the 6. When the transformation -18 vector v = the resulting vector is 54 Write down…

A:

Q: Let a = (- 6, 3) and b = (1, – 4). Compute the dot product.

A:

Q: What is the unit vector oppositely directed to 4?−5?−5??

A: Topic:-  vector algebra

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.…

A:

Q: 1. Add the following three vectors to find the resultant vector, R: šj = (-2,0)m, .ž= (0,–5,)m, .řz…

A: 1.   x1¯  =  (-2,0)mx2¯  =  ( 0, -5)mx3¯   =  (3,0)m Now , In the East - west direction ,  we deal…

Q: y = -3 7 4 6] 0 Z = 1 -8 15 -7

A: if two vectors are orthogonal, we need to compute their dot product and check if it is equal to…

Q: Given the following vectors, calculate −8u+7v U=(-3,-1),V=(7,-1)

A:

Q: Determine which pairs of vectors in Exercises 15–18 are orthogonal. 8 -2 a= [&] - [ ³ ] b = -5 -3…

A: The given vector is, a=8-5,b=-2-3. The pair of vectors are orthogonal if the dot product of the…

Q: Perform the vector addition: (– 7, 1) + ( – 12, 3)

A: Given,          <-7,1>+<-12+3>

Q: given u=5i+j+(a+2)k  and v= (3b-1)j +4j+ 6k  determine a,b so that v are parallel vectors

A: Given that, u=5i+j+(a+2)k  and v= (3b-1)j +4j+ 6k  We have to determine a,b so that u and v are…

Q: Look at the picture and the player below and try to figure out the movement of the soccer ball when…

A: Topic :- 2 Dimension

Q: A vector is written as aî + bĵ. What form is that?

A: A vector is written as aî + bĵ.

Q: Define irrotational vector. Is the vector A =(6xy+z³)i+(3x² - 2)j+(3xz² – y)k irrotational? Justify…

A: we have the vector A=(6xy+z3)i+(3x2-z)j+(3xz2-y)k we have to check weather the given vector is…

Q: Determine which pairs of vectors in Exercises 15–18 are orthogonal.

A: Two vectors u and v are orthogonal if            u.v = 0

Q: can you add 3 vectors using the parallelogram method? support you answer

A: Parallelogram law : if two vector quantity are represented by the two adjacent side of a…

Q: For the vectors u = 3ỉ − 8j + 2k and - v = 4i - 2j – 4k we have - ü × v = 28i + 20j +38k. Select…

A: The given vectors

Q: Find a vector v such that ||v||=5, and v is in the opposite direction of -5i+7j .

A: We have a vector -5i+7j Let u→=-5i+7j First, we find a unit vector in the direction of u→=-5i+7j The…

Q: Give 2 vectors of length 7 that are parallel to (-1, 2, –2).

A: Find the required vectors