Which shows the image of the figure under a translation by the given vector? ADEF with vertices D = (-5, 3), E = (-3, -2), and F = (-1, 2); b = [8, 2] :10 :F -10: -101 :10 -10 10 x -10 :10 -10: 10 x :10 D: -10: 10 x 4.

Q: Which of the following is the vector projection of (1, 0, 1) onto (-2,4,0)? 1 B. (-1,2,0) C.…

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Q: Add the vectors u (0, 3) and i = (- 2, – 1) graphically. Your graph should include u, v and the…

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Q: Find a vector a with representation given by the directed line segment AB, where A(-2, -2) and B(4,…

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Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find b.…

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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: Find a nonzero vector orthogonal to the plane through points P(2,1,5), Q(-1,2,3), and R(0,3,3), and…

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Q: The plane that contains the points (-2, 1, 0), (1,0, – 1) and (0, –1, 1) is orthogonal to which…

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Q: The orthogonal projection of the vector u=(-1,-2) on a=(-2,3) is 8 12 а) 13 13 13 b) 8 13 12 4 c) 13…

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Q: Find a vector a with representation given by the directed line segment E A(0, 3, 2), B(5,3, -5) Draw…

A: We need to find the equation from A(0, 3, 2) and B(5, 3, -5).

Q: Consider the vectors a = (-1,–2, 3), b = (3,0, –2), v = (2, –5, –4) and the plane P given by 2x + y…

A: The given vector is; a→=-1,-2,3b→=3,0,-2v→=⟨2,-5,-4⟩and Plane P is;2x+y=z+13⇒2x+y-z=13…

Q: 50. Find the vector from the origin to the point of intersection of the medians of the triangle…

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Q: Given the vectors u = (2, -2, 3) and v = (-3, 2, – 1), calculate the vector projection of u onto v…

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Q: Which of the following vectors is orthogonal to the plane 3(x - 7) + (y + 8) - 5z = 15? O O O

A: Given equations of plane 3(x-7) +(y+8)-5z=15this is an equation of the form a(x-x1)+b(y-y1)+…

Q: The vector projection of u = [3, -4, -2] on the x-axis is: %3D 3 29 3 29 3í

A: The direction ratios of the X-axis are, (1,0,0) Also, u•(1,0,0) = 3 is the scalar projection on the…

Q: (e) 5. Compute the angle between the vectors [1, –1,0, 1] and [0, 1,0, 2]. 6. Compute the…

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Q: Write the projection of 2î +3j-k along the vector î+j.

A: Given that: 2i+3j-k along the vector i+j.

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: The parallelogram shown here has vertices at A(2, -1, 4),B(1, 0, -1), C(1, 2, 3), and D. Find the…

A: given: a figure showing parallelogram having the vertices A(2,-1,4), B(1,0,-1), C(1,2,3) and D. we…

Q: Give the terminal point of the position vector of u= (3,4). Clearly show why your answer is…

A: Given that Position vector of u→=3,4 So, graphically it is as below:

Q: Q1. If O (0,0,0) in (x,y,z) 3-D space and r(2,5,1) draw the vector in 3D and find its direction.

A: Plot point in 3D

Q: Find a vector a with representation given by the directed line segment AB. A(-4, -2), В(2, 5) Draw…

A: A vector from point A (x1,y1), to point B (x2,y2) is given by AB =(x2-x1)I +(y2-y1)j

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: 3. For the vectors b= (2, -1, -2) and a = (0, 4, –3) (a) Compute the projection of vector b onto the…

A: Consider the equation

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: Given the vector u = (4, 1, -6) and a = (1, O, 5). The orthogonal projection of u on a (projau ) is…

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Q: 4. If the position vectors of the three points A, B and C are (2, 4, -1), (1, 2, -3) and (3, 1, 2)…

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Q: The Nector goes from P = (2,0) to Pq = (-2,3). The A goes from and t W, Q=(2,0) to Q= (5,-1). Dran…

A: Vector addition

Q: For vectors ā = (2,4,-1), b =(-1,3,2), calculate the vector projection of b on ā. %3D

A: Vector projection of b→on a→=(a→.b→)a→Consider  a→.b→=(2×(-1))+(4×3)+((-1)×2)…

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: 22. Given that the vectors a = 3i-4j-4k, b = 2i-j + 3k, and c = 4i-3j +5k. The %3D %3D projection…

A: Here let d= a+b d= a + b⇒d = 5 i -5j -kProjection length of vector d = (a+b) on c is given by |d|…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Given, A=( 1,1,0 ); B=( -2,3,-4 ); P=( -3,1,6 )To find: Distance from point P to the line through A…

Q: 1 Consider the line through the vector a = Find the project of b = (1,2,3) onto this line.

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Q: Find the vector w which is of length 6 and oppositely directed to u=(2,-2,1) Select one: O None W=…

A: A vector oppositely directed to  u⇀ = <2,-2,1>  is  w = − u = − <2,-2,1>  i.e.  w =…

Q: Let ri = xi+yıj+z¡k, r2 = x2i+ Y2j + z2k and r3 = x3i+ Y3j + z3k be the position vectors of points…

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Q: Find a vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2)

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Q: Use vectors to decide whether the triangle with vertices P(1,-3,-2), Q(2,0,–4) and R(6,–2,-5) is…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: ) Find a vector equation for the line that goes through the points (7, 6, 2) and (2, 14, 2). F(t) =…

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Q: 1 Which vector is perpendicular to the plane -2x + 3y – 4z = 9? 1 1 2' 3 О 2, -3,4] 2 1 9 3? О 12,3,…

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Q: Determine whether the vectors {(1,-1,2).(-1,1,2).(0,0,1)} span R3. If they do, give the linear…

A: To discuss the linear independence (or otherwise) of the given vectors and describe their span

Q: Consider the lines L1 and L2 in R³ given by the vector equations L1 :ở = (2,4, 4) + t(4, 1, 5) and…

A: Given: L1 : v→ =2 , 4, 4+t 4, 1, 5 And  L2 : v→ =1, -3, 2+t -2, 3, 1

Q: )P=(3,2,1), then the parametric equation of the line is :   a.

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Q: 3. Find a vector equation of the line going through the point A(4, -5, 2) that is orthogonal to both…

A: The detailed solution is given in the next steps.

Q: Which of the following vector is perpendicular to the plane 2x - 3y + 5z +7 = 0? O1-6, 1, 3] O [2, -…

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Q: EXAMPLE 2 Find a vector perpendicular to the plane of P(1, –1, 0), Q(2, 1, –1), and R(-1, 1, 2)…

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Q: Find the orthogonal projection of the vector a (-9,-8, 7) in the direction of the (-3,-5,-2). vector…

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Q: Find an equation of a plane passing through the given point and perpendicular to the given vector.…

A: The plane is perpendicular to the given vector 8,3,2. So the direction ratio of the normal vector to…

Q: Find an equation of a plane passing through the given point and perpendicular to the given vector.…

A: The equation of the plane perpendicular to the vector <a, b, c> is: ax+by+cz+d=0 Therefore,…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Let us consider a line l joining by  two points A  and B. Consider a point P (not on line l ) then…

Q: 2. Determine the vector equation of the plane that contains the following two lines. L1: 7 = [ 4,…

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