a) Write an algebraic rule that would translate a figure 15 units right and 13 units down. (x, y) → (. b) Write the components of a vector that would translate a figure 14 units up.(L_

Q: Give a vector description of the midpoint M of a line segment AB.

A: According to the vector midpoint formula: Where 'c' is the midpoint position vector of vector 'a'…

Q: Find equations for the planes The plane through A(1, -2, 1) perpendicular to the vector from the…

A: The normal vector of the plane is given by A(1,-2,1)  The point of passing is (0,0,0). The equation…

Q: What is the terminal point of the vector a = <1, 3> based at P = (2, 2)? Sketch a and the…

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

Q: In Cartesian space, the direction of the line (x, y, z) = (a, b, c) +r(d, e, f) is represented by…

A: The given line is (x,y,z)=(a,b,c)+r(d,e,f) So, the point (a,b,c) is on the line and (d,e,f) is a…

Q: 10 Find the vector equation of a line whose symmetric equations are z-1 y+3 %3D 3. -4 Express your…

A: To find the vector equation of a linewhose symmetric equations are   x-12=y+33=z-1-4.

Q: Find the resultant using (a) the parallelogram method, and (b) by summing up components. For the…

A:

Q: Find the angle between the planes whose vector equations are 7-(2i + 2)- 36) =57-(3i -3) + Sk) = 3…

A: The solution to the the given question is explained below.

Q: The unit vector in 2-space that makes an angle of π/3 with the positive x-axis is _____

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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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Q: Find an equation of the plane through the point and perpendicular to the given vector. (8, 2, 3)…

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

Q: Let the vector 3i +j can be expressed as a sum of vectors u and v where u is parallel to the vector…

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Q: Write the vector v = ⟨2, -4, 4⟩ as a product of its magnitude and a unit vector with the same…

A: Given vector is  v=2,-4,4 Magnitude of vector v  is v=(2)2+(-4)2+(4)2=4+16+16=36=6 Now, unit vector…

Q: Find the vector v that has a magnitude of 10 and a direction oppo- site that of the unit vector…

A: Let u be the required vector and given vector be v=35i-45k.

Q: Describe the Z-axis in R as the span of a vector. Can you describe it as the span of other vectors…

A:

Q: 4. Identify the component form of the vector that maps AABC to its image AA'B'C' A. B. 2 C. D.…

A: Given graphs  1) vector that maps  triangle ABC has vertices A(3,-1),B(7,-3),C(1,-6) to its image…

Q: Find u + v, u-v, and 3u - 4v. Then sketch each resultant vector. =(3,2), v = (2, 5) %3D

A: Given that u=3,2 and v=2,5 find  a) u+v b) u-v c) 3u-4v

Q: Rotate the vector (0,2) 270° counter-clockwise about the origin. {[ ? ],[ KU?1| )

A: Given vector is : 0,2 , rotate the vector 0,2 270∘in counter clockwise about origin.

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: 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: Let a point a = (2, 4, 5). %3D Find a unit vector (just one) that is orthogonal to a.

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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: Write, in your notebook, which vectors are represented in the Cartesian plane.

A: We know that, the position vector AB → between the points Ax1,y1 and Bx2,y2 is given by  AB→=x2-x1…

Q: True or False A vector in space may be described by specifying its magnitude and its direction…

A: Answer: True.

Q: V. 3. V3

A: We have to solve given problem;

Q: Find an equation of the plane through the point (29,-37,46) and with normal vector 14i+19j–17k.

A: we have to find an equation of the plane passing through the point (29,-37,46) and with normal…

Q: Find a unit vector perpendicular to the plane ABC if A (2,-2,1), B (3,-1,2) and C (3,-1,1)?

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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: Find the vector v and illustrate the specified vector operations geometrically, where u = (−2, 3)…

A: We need to find vector v for which  If, u = (−2, 3) and w = (−3, −2)

Q: Write a DAG model for computing the dot product between twon-dimensional vectors r and y.

A: Let,  x→=x1i^+x2j^+x3k^y→=y1i^+y2j^+y3k^

Q: 7. Write the vector w in terms of u and v, given that the terminal point of w bisects the line…

A: This question is related to vectors, we will solve it using given information.

Q: Write the vector v in terms of i and j whose magnitude Iv] and direction angle 0 are given. Ivl - 7,…

A: This question can be solved using the concept of component form of vectors.

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: Write the unit vector v in compa sketch. a) Ivl = 8,0 = 45

A: a)v=8, θ=45

Q: Find the vector v, where u = (-1, 3) and w = :(-3, -1). v = u + 2w Illustrate the specified vector…

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Q: Find the measures of the angles of the triangle whose vertices are A = * .(-1, 0), B = (2, 1), and C…

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Q: 1. What is the appropriate dot product technique for both Cartesian and Geometric vectors?

A: Given

Q: Draw the vector V that goes from the origin to the given point. Then write V in componentform (a, b)…

A: Consider the given point 1,4 and origin 0,0

Q: Determine if the vectors u=, *v= and w= lie in the same plane or not

A:

Q: 4. Identify the component form of the vector that maps AABC to its image AA'B'C A. B. C. D. ぐ 21…

A: first we write thev coordinate of the vertex of each trangle

Q: Find the vector in vl that has magnitude 8| and is in the opposite direction of (-3, –5, 1). v =||…

A:

Q: Give a vector description of the midpoint M of a line segment AB→.

A: GivenLine segment AB→To find vector description of midpoint of AB

Q: If a vector V is in standard position and the tip of the vector corresponds to the point(a, b), then…

A: Given, If a vector V is in standard position and the tip of the vector corresponds to the point(a,…

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…

Q: Two vectars'a and -b are given as a =i+2j + kandb= 3i + j + 2k. The vector product ax.b is

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Q: a b

A:

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

A: