In Exercises 25-30, express each vector as a product of its length and direction. 2i + j - 2k

Q: Use the figure to find the specified vector. Find -a. OT -10-8-6 6'8 10X -161 (-3,-7) O (7,-3) O…

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Q: Consider the vectors [2, 1,0, 2|], [3, 1,0, 1), [1,1, 0, -1] in R. Decide whether they independent.…

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Q: C A

A: We use Triangle law

Q: Find a unit vector u in the direction opposite of (–10, –5, –9). u =

A: Let v=-10,-5,-9 So, the unit vector in the opposite direction is,   u=-v→-v→

Q: Consider the vectors (2, 1, 0, 2], [3, 1,0, 1], [1, 1, 0,-1] in R'. Decide whether they independent.…

A: Given: Vectors in ℝ4,                              2,1,0,2, 3,1,0,1, 1,1,0,-1 To find: Whether the…

Q: In Exercises 13-18, determine whether the two vectors are orthogonal and, if not, whether the angle…

A: Solved below

Q: express each vector as a product of its length anddirection. 2i + j - 2k

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Q: In Exercises 5-12, sketch each vector as a position vector and find its magnitude. 5. v = 3i + j 7.…

A: We’ll answer the first question (that is 5) since the exact one wasn’t specified. Please submit a…

Q: What is the staring point of the vector i = -3i + 2j, if the ending point is (-2, 1)? %3D A ( 5,3) B…

A: Given: v=-3i+2j , ending point -2,1 Let the starting point x,y. We can find the position vector by…

Q: Determine whether the statement"If u = ai + bj is a unit vector, then a2 + b2 = 1." is true or…

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Q: Show that Il all = 11b|l Are the vectors ã' and b equal?

A: ||a|| = ||b|| a and b are not equal.

Q: What is the staring point of the vector i = -3i + 2j, if the ending point is (-2, 1)?

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Q: In Exercises 53-56, let u = -2i + 3j, v = 6i – j, w = -3i. Find each specified vector or scalar. 53.…

A: 53). Given vectors are u=-2i+3j, v=6i-j, w=-3i. To find: 4u-2v-w Solution: We know that scalar…

Q: Find the magnitude of the vector. (-3, – 7)

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Q: Give vectors a, b, c, d such that a=5c + 3d and b= 2c - d express 2a - 3b in terms of c and d

A: Solution as given below:

Q: Determine the figene valves and Vector for 2 A=-1 2 -2

A: (A-λI)X=0 A= given matrix λ=constant I=identity matrix

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: Express the vector in the form (a, b). 1(i + j) ji + jl

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Q: 2) (Section 9.4/9.5) Determine the value of 'a' that would make the vectors perpendicular u = and v…

A: For the vectors to be perpendicular  Then the dot product of two vectors is zero.

Q: Show that the vectors are orthogonal.

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Q: Express the vectors in Exercises 13 and 14 in terms of their lengths and directions. 13. 2i - 3j +…

A: 13.Given vector is 2i - 3j + 6k.

Q: In exercises 7-10, list seven vectors in Span {v1, v2}. For each vector, show that the weights on vi…

A: Finding the vector span and describing the geometric description of the span

Q: 2. Determine the value of a for which the vectors b = ai – 5j+3k and 7 =i +2}-ak are orthogonal ?

A: Orthogonal Vectors: two vectors are orthogonal if they are perpendicular to each other. i.e. the dot…

Q: In Exercises 25–26, express each vector as a product of its length and direction. 25. 5k 26.…

A: We’ll answer the 25th question since we answer only one question at a time. Please submit a new…

Q: 6. A student claims to have found a vector A such that (2i - 3j + 4k) x A = (4i + 3j - k). Do you…

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Q: In Exercises 87-90, let v = i - 5j and w = -2i + 7j. Find each specified vector or scalar. 87. v + w…

A: # We are entitled to answer three sub-parts. Please resubmit the question which you wish to get…

Q: Determine by inspection whether the vectors in Exercises 15-20 linearly independent. Justify each…

A: The given vectors are v1=4-26,v2=6-39.

Q: What is the terminal point of the vector a = (4, 1) based at P = (1, 5)? Answer:

A: Use the definition of terminal point, we solve this problem as in next step.

Q: Give an example of vectors in R^3 that spans R^3. (show works)

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Q: In Exercises 57–60, let u = a,i + bj v = azi + baj w = azi + baj. Prove each property by obtaining…

A: Given vectors are: u=a1i+b1j, v=a2i+b2j and w=a3i+b3j 57). To prove: u+v=v+u Proof:…

Q: Find a unit vector parallel to the vector a´. a'= (-2,3,–1)

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Q: Show that if u and v are vectors in the three-space, then ||u x v||? = ||u|| ||||² – (u · v)²

A: u and v are vectors.

Q: Sketch the vectors

A: Solution : The magnitude  of |a| , |b|, |c| are  |a|=a1+a2|b|=b1+b2|c|=c1+c2 a=(-3)2+22     =9+4…

Q: Determine whether the vectors a = 2i-3j+ 5k, b 3i+j-2k and c=i-7j+12k are linearly dependent or…

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

Q: determine the magnitude of the vector ∥⟨2,8⟩∥

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Q: Define the vector?

A: we have to define the vector.

Q: Find the length of the vector. v - (9, 12)

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Q: Use vectors to determine whether the points (3,4,-1), (-1,6,9) and (5,3,4) are collinear.

A: The points (3,4,-1), (-1,6,9) and (5,3,4)

Q: Express the vector in the form (V= ai+ bj+ck) *, if A(1,0,3) and B is (-1,4,5):

A: Vector from

Q: What is the resultant of vectors a and b? (

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Q: Express the vectors in Exercises 9–10 in terms of their lengths and directions. 9. 22i + 22j  10. -i…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Repeat the directions of Exercise 3 with the same vector w, but with u, = uz = -2 u = u u = |-3 9-…

A: Please find the answer in next step

Q: Consider the vectors (2, 1,0, 2], (3, 1,0, 1], [1, 1,0, -1] in R'. Decide whether they independent.…

A: Given: Vectors in ℝ4,                              2,1,0,2, 3,1,0,1, 1,1,0,-1 To find: Whether the…

Q: In Exercises 25–26, express each vector as a product of its length and direction. 25. 2i + j - 2k…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: 64. Show that if u + v and u – v are orthogonal, then the vectors u and v must have the same length.…

A: here, the given vectors, A =u+vB=u-v given that, they are orthogonal, that is, A·B=0u+v·u-v=0⋯⋯1

Q: Determine the dot product of the vectors а 3 (-3,—2, 3), b %3D (2,1,-2). b = (2,1,–2). a = 1. а:b —…

A: Solve for dot product

Q: The scalar projection of the vector 7 = (-2, 3, 1) on 7= (2m, -1, 3) is -1. Determine the value of…

A: Follow next step

Q: In vector form (as in Exercises 5 and 6), find an equation for the line through the point (4, – 3,…

A: Given: The line passing through the point 4,-3,7 and with direction vector 4,2,-3. Concept used: The…