When do directed line segments in the plane represent the same vector?

Q: Find a vector å with representation given by the directed line segment AB, for A(0,3,1) and B(2,3, –…

A: We have to find the vector and draw it.

Q: 6. If u,v, and w are three vectors in R', describe their linear span.

A: 6. If u,v and w are three vectors in R7, we have to describe linear span.

Q: Define the term Parallel Vectors?

A: Parallel vectors: The vectors that are parallel if they have the same direction.

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: 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: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(3, 4, 5) P2(2, 3,…

A:

Q: Find the unit vector represented by the directed line segment with initial point A (-2,1,1) and…

A: The vectorAB = B-A=(2,-3,4) -  (-2,1,1) = (4,-4,3) So the unit vector is :…

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

A:

Q: Define the points P(-4, 1), Q(3, -4), and R(2, 6).

A: The given points are The vector QP is So, the unit vector (v) of QP is

Q: photo attached

A: Given that a vector V goes from the origin to a point (5, -5).

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: Use vectors to show that the points form the vertices of a parallelogram. (2, 9, 1), (3, 11, 4), (0,…

A: Given: A=(2,9,1) ,B=(3,11,4),C=(0,10,2),(1,12,5) To Show: Given points form the vertices of a…

Q: Find a vector a with representation given by the directed line segment AB, where A(-4, 0, 1) and…

A: A=-401,  B=18-1 the vector a is given by  a=B-A

Q: A plane contains the point  (1, -1,0 ) and its normal vector is \ vec {n} =  (6,24, -8 ). What is…

A:

Q: Find a direction vector for the line through (4, 5, 3) and (2, – 3, – 1).

A: to find the direction vector

Q: Suppose L1 and L2 are disjoint (nonintersecting) nonparallel lines. Is it possible for a nonzero…

A: Given:

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

A: To determine the point of intersection of the medians of the triangle.

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(0, 0, 0) P2(2, -2,…

A: To find:(a) the direction of vector P1P2(b) the midpoint of line segment P1P2P1(0,0,0) and…

Q: If vector v is represented by an arrow, how is -3v represented?

A: Given: If vector v is represented by an arrow. To find: How is -3v represented?

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: Draw an example of two opposite vectors that are not parallel or explain why such vectors don't…

A: To find: Two vectors opposite in direction which are not parallel. or, Explain why above two vectors…

Q: What is the length of the vector (1, 4, 5, -3) in R^4?

A:

Q: 2. Use a directed line segment to represent the vector. (а) и %3D (2, —4) (b) v = (2,4, –4)

A: Given that the vector a u=2,-4  b v=2,4,-4Solution a u=2,-4u=22+-42u=20  =25b v=2,4,-4v=22+42+-42v=6

Q: Give an example of a non zero vector that is perpendicular to (5,7,4)

A: We know that "two vectors are perpendicular to each other if and only if their dot product is zero"…

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: Construct a geometric figure that illustrates why a line in R2not through the origin is not closed…

A:

Q: How many different direction vectors does a line have?

A: Query - How many different direction vectors does a line have? Answer- Direction numbers is a number…

Q: Which vectors, drawn on a grid from one point (on the "cross-hairs") to another have integer values?

A: Y-component of A →…

Q: We define a median vector of a triangle to be the vector from a vertex of the triangle to the…

A: Let ,The triangle be ∆ABC A(x1, y1, z1)B(x2, y2, z2)C(x3, y3, z3)AM→ , BM→ , CM→ be the medians

Q: Let vector AB = (2,3,1). If the coordinates of A are (2,1,5), what are the coordinates of the point…

A: Vector AB= B-A

Q: Use vectors to prove that the line segment joining the midpoints of two sides of a triangle is…

A: Using Vectors, Our Aim is to prove that the line segment joining the midpoints of two sides of a…

Q: Show that the vector v = ai + bj is perpendicular to the line

A: GivenVector V = ai + bj and the line ax + by + c

Q: Find a vector å with representation given by the directed line segment AB, for A(-1, 1) and B(3, 2).…

A:

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

A:

Q: Use a directed line segment to represent the vector.v = (−2, −5)

A: Let the given vector : Here, -2 represents x-cordinate and -5 represents y-cordinate.

Q: Suppose that a parallelogram is bounded at one vertex by the vectors i = |,3 = ,: Find the area of…

A: Area of parallelogram =|u×v| ,where u and v are the vectors which represent the side of…

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

A:

Q: Determine whether Hhe Lindependent. by inspection Vectors are linearly 6. -2 -3

A: A vector is given

Q: Use a directed line segment to represent the vector.u = (2, −4)

A:

Q: The sum of two vectors is called the ___________, and it can be represented geo-metrically as the…

A: The sum of two vectors is called the resultant, and it can be represented geometrically as the…

Q: Find the vector v in the plane represented by the directed line segment from (4,-3) to (-2,6)

A:

Q: Use vectors to show that the triangle with vertices (-2, 2), (4, 10), and (20, –2) is a right…

A: vector method to find right angle triangle.

Q: ) Below is a diagram of the dotted cube with edges of length 5. Suppose (5, 0,0), v = (0, 5, 0), and…

A: Given u=5,0,0v=0,5,0w=0,0,5

Q: Show that direction vectors of the lines L: and are arthogonal.

A:

Q: Use a directed line segment to represent the vector.u = (−3, −4)

A: The directed  line segment is the vector drawn from the any two points in the cartesian plane. The…

Q: Consider the plane that goes through the point (4, 1, 3) I to vector (2, 3, 1).

A: It is given that the plane is passing through the point (4,1,3) and orthogonal to the vector (2,3,1)…

Q: Find a vector equation for the line segment from (2, -1, 4) to (4, 6, 1)

A: