In Exercises 25–26, express each vector as a product of its length and direction. 25. 2i + j - 2k 26. 9i - 2j + 6k

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

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Q: In 3-D, let L be a line that does not pass through the origin. let v1, v2, and v3 be three vector…

A: We have to decide there vectors v1, v2, v3 are linearly indipendent in R3 or not.

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: Consider the points A(1,-5), B(-1,3) and K(4,-2) in 2D. A. Determine the vector AB B. Determine the…

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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.…

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Q: (c) Are the vectors = (3, 1, 2, 1), v2 = (-1,0,1,0), 03 independent? Explain why. (3,0,0,3), v4 (5,…

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Q: Find a vector a that has the same direction as (-8, 5, 8) but has length 3. Answer: a =

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Q: Consider vectors, 2 u = |2, v = w = |-3 (a) Do these vectors line in a plane ? Why? Why not? Find…

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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: Find the angle between the two vectors and determine if they (section 9.5/9.6) are orthogonal: BAGU…

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Q: 5) Write the analytical expression of the unit vector for F= 400 i + 700j - 400 k %3D

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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: What is the terminal point of the vector a = (2, 2) based at P = (2,4)?

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Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, –1)

A: the given vectors are: u=-8,-6,4v=17,-18,-1 we have to find a unit vector that is orthogonal to both…

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: 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: 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: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, -1)

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Q: Use paper and pencil to identify the redundant vectors. 2 1 3. 4. 3. 4.

A: We have to identify redundant vectors.

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

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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: Let the vector be x = (5,6), determine its coordinates relative to the base B = {(1,1),(-1,2)}}

A: Introduction: When a basis is provided, one can represent a vector belonging to the precise vector…

Q: a. Without doing any calculation, explain why one might conjecture that two vectors of the form (a,…

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Q: what is the terminal point of a vector with initial point that Ar (-1,0is equivalent to u 3,4 O B3)…

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Q: Which vector below is NOT orthogonal to i = -2î – 8ŷ + 7k ? -- 1 2 8. O 0 î + 0ĵ + 0k 3. 1 O 4 î - )…

A: Given problem:-

Q: . Prove that (only one): E - 4y-V3ay is a unit vector? a- F 2 b- A = 6ax - 3a, + 2a, and B = 3a, +…

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Q: 4. Give an example of vectors in R3 that spans R3. (show works)

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Q: write the given vector in terms of I and J. u={-8, 10} u=???

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Q: 10. Which of the vectors U =, V = and W = are in the same plane?

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Q: Find a unit vector in the direction of u = (5, 3, 2).

A: Given vector is u=(5,3,2) Find a unit vector

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: The length of the vector c = (2, -3, 1) is %3D

A: Length of vector equal to magnitude of that vector  if v = <x,y,z>  then magnitude/Length =…

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: For Exercises 19–28, use vectors u = (-4, 1) ,v = (5, -2) , and w = (0,6) to perform the indicated…

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Q: Which vector is the result of a + 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: Determine whether the vector U = 2 is a linear combination of the vectors Xi = 2 X2 = and X ? Give…

A: Let  U→=aX1→+bX2→+cX3→  Where, a,b and c are scalar. Then,…

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Q: What is the component form of the vector represented by 2a when = (-2, 3)? Enter the answer in the…

A: If we multiply by a constant to any vector then  magnitude of that vector will be changed.

Q: Show that if A⋅(B×C)=0, the three vectors must lie in the same plane.

A: We have to show that if A ⋅ (B × C) = 0 then all three vectors A , B , and C lies in the same plane.…

Q: The unit vector of u = [3, 4, 12] is:

A: Given:u⇀=3,4,12

Q: Describe a unit vector in R^3 with the same direction as <1,0,7>

A: Consider the given point vector

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) (10, -12, -2) %3D V =

A: Find the unit vector that is orthogonal to both u and v

Q: In Exercises 1–5, find the length and direction (when defined) of u * v and v * u. 1. u = 2i - 2j -…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…