In Exercises  14, the initial and terminal points of a vector are given. (a) Sketch the directed line segment. (b) Find the component form of the vector. (c) Write the vector using standard unit vector notation. (d) Sketch the vector with its initial point at the origin.  14. Initial point: (6, 2, 0) Terminal point: (3, −3, 8)

Q: Write expressions for the scalar and vector projections of vector b Illustrate with diagrams?

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A: Consider the provided information, The component vector v=PQ→ where P=a1,b1 and Q=a2,b2 are…

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A: The initial point is (3, -5) and the terminal point is (8, 6)

Q: Find the component form and magnitude of the vector v. Initial Point Terminal Point (17, -3) (9, 5)…

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Q: What is the unit vector for the vector (-9.53, 13.04, –13.15)? Answer: ( Nete

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Q: 10. Find the vector equation of a line whose symmetric equations are x-1 y + 3 z- 1 %3D %3D 3…

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A: We will find an equation of the plane through the point (8,2,3) and perpendicular to the given…

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A: Given :           The vectors are 10-1 , -110 , 0-11   To describe the span of the given vectors…

Q: In Exercises 21 and 22, find the equation of the line containing the given points in slope–intercept…

A: Given, P(0,5), Q(2,-1) slope of line between this point m=-1-52-0=-3 equation of line is…

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

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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: Find the length of the vector a %3D

A: The length of a vector x→=abc is given by the equation; ||x→||=a2+b2+c2

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Q: Determine the tail of the vector whose head is(1, 2). Make a sketch.

A: Given the vector 26 and tail of the vector is (1,2). We need to find the head of the vector.

Q: Given a vector with initial point (−8, 3) and terminal point (5, −5), find an equivalent vector…

A: In the question we have to find an equivalent vector with initial points (0,0).

Q: 3. Write the vector (1, 1, 1) as a linear combination of a vector in the direction of (2, –2, 1) and…

A: We have, a→=(1, 1, 1) and u→=2,-2, 1 Let b→ is vector in the direction of u→=2,-2, 1 So, b→=λ2,-2, 1…

Q: A figure is translated using the vector (-3, 7). What translation vector would move the image back…

A: i have provided solution in step2

Q: the initial and terminal points of a vector are given. (a) Sketch the directed line segment. (b)…

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

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Q: V. 3. V3

A: We have to solve given problem;

Q: Determine the head of the vector;whose tail is (−3, 2). Make a sketch.

A: Consider (x, y) as the head of the vector. Then  -25=xy--32-25=x+3y-2

Q: describe the span of the given vectors a)geometrically b)algebraically

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Q: Let A = (0, 0, 0) and vector v = (-3, 0, 1). Find vector equation of the line containing the point A…

A: Given point on the line is A=(0,0,0) and the line is parallel to the vector V=(-3,0,1)

Q: Define the vector?

A: we have to define the vector.

Q: In Exercises 35–38,  find an equation for the line through P perpendicular to v. Then sketch the…

A: given an equation for the line through P perpendicular to v

Q: Determine the tail of the vector whose head is (1, 2). Make a sketch.

A: Consider the provided vector, 26 Whose head is 1,2. Determine the tail of the given vector.

Q: Find the component form and the magnitude of the vector v. Initial Point Terminal Point (-4, 6) (24,…

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Q: Find the magnitude of the resultant vector. (-25.6, 7.7)- (-11, -9.8) 1R

A: letA→=-25.6, 7.7 and B→=-11,-9.8

Q: Write the component form of a vector v with initial point P(8.6, -2.5) and terminal point Q (6.7,…

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Q: Express the vector v with initial point P and terminal point Q in component form. (Assume that each…

A: From the graph we can se that the coordinates of point P is 5, 2 and the coordinates of point Q is…

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A: Given,r→=-2,0+t7,-5r→=-2,0+7t,-5tr→=7t-2,-5t................(1)we…

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…

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Q: Find the component form and the magnitude of the vector v. Initial Point Terminal Point (-4, 6) (17,…

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Q: 1. what is the basic concept of a vector?

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Q: Exercises 39–42,  find an equation for the line through P parallel to v. Then sketch the line.…

A: Since we only answer up to 1 question, we’ll answer the first question. Please resubmit the question…

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Q: Write the vector equation of the line in space using vector properties and show it in the figure.

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Q: find the component form of the vector. The vector from the point A = (2, 3) to the origin.

A: Find the component form of the vector. The vector from the point A = (2, 3) to the origin.

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: 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…