Question

Find a vector equation for the line segment that joins P(1,3,4) to Q(-2,4,6)

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Linear Algebra: A Modern Introduction

4th Edition

ISBN: 9781285463247

Author: David Poole

Publisher: Cengage Learning

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Linear Algebra: A Modern Introduction

Vectors. 21EQ

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Q:Ā Determine the vector equation for the line that is parallel to = [1,5,-7]+[2,-1,5] with the sameā¦

A:Ā The general equation of line in vector form isĀ Ā .Then note the result : Line passing through theā¦

Q:Ā Find a vector equation for the line that goes through the points (5,9,0) and (0, 11, 1). F(1) = withā¦

A:Ā A ( 5,9,0) B ( 0,11,1)

Q:Ā Find the vector equation of the line that passes through point M(1, 1, 2), intersects the followingā¦

A:Ā Question is solved.

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

A:Ā Given: Let A(7,6,2) and B(2,14,2) be the two points the line passes through To find: vector equationā¦

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

A:Ā Click to see the answer

Q:Ā Find a vector equation with parameter t for the line through the points (ā1, ā7, ā4) and (-9, 8, 2).

A:Ā we know that vector equation of line which passes through pointsx1,y1,z1,x2,y2,z2 is given byā¦

Q:Ā Find a direction vector for the line containing the origin (0, 0, 0) and the point (2, 3, ā 1).

A:Ā The given points areĀ 0,0,0Ā Ā andĀ Ā 2,3,-1

Q:Ā Find the symmetric equation for the line through the point of (2.-5,4)and a vector (3,ā1,-3).

A:Ā Given the vector is, 3,-1,-3 And the point is, (2,-5,4). The parametric equation forā¦

Q:Ā Explain how to find a vector in the direction of the line segment from P0(x0, y0, z0)Ā to P1(x1, y1,ā¦

A:Ā Initial point isĀ P0x0,Ā y0,Ā z0 and the terminal point is P1x1,Ā y1,Ā z1.

Q:Ā Find a direction vector for the line containing the points (-1, 5, 2) and the point (2, 3, ā 1).

A:Ā Given, A=-1,5,2B=2,3,-1

Q:Ā | Find a vector equation for the line through the point (ā9, ā9, 3) parallel to the line 19 + 4t, yā¦

A:Ā Click to see the answer

Q:Ā Find the vector that has the same direction as (6, 2, -3) but has length 2.

A:Ā Click to see the answer

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

A:Ā Click to see the answer

Q:Ā Find the vector that has the same direction as (3, 2, -6) but has length 5.

A:Ā Just follow the flow and you are done.

Q:Ā Find a vector equation for the line segment connecting the points P = (-9,ā6, 8) and Q = (-15,ā¦

A:Ā We have to find a vector equation for the line segment connecting the pointsĀ P=-9,-6,8Ā andā¦

Q:Ā Find the vector that has the same direction as (3, 6, -2) but has length 5.

A:Ā One given vector is (3, 6, -2) Length of another vector = 5

Q:Ā Find the vector that has the same direction as (2, 6, -9) but has length 4.

A:Ā Click to see the answer

Q:Ā Find a vector equation for the line through the point (-6, 4, 1) perpendicular to the vectors u =ā¦

A:Ā A line passes through the pointĀ -6,4,1 and perpendicular to the vectorsĀ uā=-1,-2,3 andĀ vā=3,-8,-9 Weā¦

Q:Ā Give the vector equation of the line passing through P and Q.P = (1, 1, 0), Q = (1, 0, 1), R =ā¦

A:Ā P=(1,1,0)Ā andĀ Q=(1,0,1)weĀ haveĀ toĀ findĀ vectorĀ equationĀ ofĀ theĀ lineĀ passingĀ throughĀ theseĀ points

Q:Ā Sketch the vector b = <3, 4> based at P = (ā2, ā1).

A:Ā SketchĀ theĀ vectorĀ b=<3,Ā 4>Ā basedĀ atĀ P=(ā2,Ā ā1).

Q:Ā Find a direction vector for the line containing the points (-1, 5, 2) and the point (2, 3, - 1).

A:Ā We have to find a direction vector for the line containing the pointsĀ -1,Ā 5,Ā 2 andĀ 2,Ā 3,Ā -1. We knowā¦

Q:Ā find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(-1, 1, 5) P2(2, 5,ā¦

A:Ā GivenĀ PointsĀ -Ā P1Ā =Ā -1,Ā 1,Ā 5P2Ā =Ā 2,Ā 5,Ā 0VectorĀ P1Ā andĀ P2Ā ,P1āĀ =Ā -i+j+5kā¦

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

A:Ā Click to see the answer

Q:Ā find the components of the vector PQ. P = (-}, 3, 1), Q = (4, 6, 0)

A:Ā P=-12,Ā 92,Ā 1,Ā Ā Q=4,Ā 6,Ā 0

Q:Ā Find the vector equation of the line (a) through the point (1, ā5) and parallel to the x-axis; (b)ā¦

A:Ā As per our guideline we are allowed to do 1 question and 3 subparts at a time. Please post otherā¦

Q:Ā find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(1, 4, 5) P2(4, -2,ā¦

A:Ā Given thatĀ P1Ā 1,Ā 4,Ā 5Ā Ā Ā andĀ Ā P2Ā 4,Ā -2,Ā 7. Compute the direction of vector P1P2 as follows.ā¦

Q:Ā Find an equation of the line that goes through A(0, 1, 4) and is orthogonal to the Y-axis and vectorā¦

A:Ā Click to see the answer

Q:Ā Find the vector in the same direction as <1, 1, 0> whose component in the direction of <2,ā¦

A:Ā Let Ā us suppose that

Q:Ā Find the magnitude of the projection of (- 1, 2) onto the vector (3, 5)

A:Ā Click to see the answer

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

A:Ā Click to see the answer

Q:Ā Find the distance of point 4(2-/3,2) from the line that passes through the origin and parallel toā¦

A:Ā Distance of a pointĀ A(x1,Ā y1) from the lineĀ ax+by+c=0 is given byĀ d=ax1+by1+ca2+b2

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

A:Ā If given two vectors the vector perpendicular to both the vectors is given by their cross product.ā¦

Q:Ā The vector equation for the line passing through the points (-4, 1,0) and (4, 4,-3) is r(1)-

A:Ā It is given that the line passes through the points (-4,1,0) and (4,4,-3). Consider that the vectorā¦

Q:Ā Find the unit vector represented by the directed line segment with initial point AĀ (-2,1,1)Ā andā¦

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

Q:Ā What is the vector between the point (ā3a,ā7b) and the point (ā4a,ā5b)?

A:Ā Vector between two points A and B is B-A

Q:Ā Find a vector a that has the same direction as (-8, 9,8) but has length 3.

A:Ā The solution is given below

Q:Ā Find the distance of point 4(2/3,2) from the line that passes through the origin and parallel to theā¦

A:Ā follow next step

Q:Ā Find the vector from the origin to the point of intersection of the medians of the triangle whoseā¦

A:Ā Concept: The calculus involves the study of rate of change, which is used to calculate the objectsā¦

Q:Ā Find the vector from the origin to the point of intersection of the medians of the triangle whoseā¦

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

Q:Ā photo attached

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

Q:Ā Find two vectors v1 and v2 whose sum is , where v1 is parallel to while v2 is perpendicular to . v1ā¦

A:Ā Click to see the answer

Q:Ā Use the vectors u = (1,-3,5) and v=(2,1,-3) to Find The equation of the line through (1,2,3) withā¦

A:Ā Given vectors u=(1, -3, 5)Ā v=(2, 1,-3)Ā And line passing of point (1, 2,3)

Q:Ā Find the vector of length 2 making an angle of 60Ā° with the x-axis.

A:Ā Click to see the answer

Q:Ā A vector is 0.888 m long and points in a 205 degree direction. Find the y-component of the vector.

A:Ā Click to see the answer

Q:Ā The terminal point of the vector v = i +2j +3k with initial point (4, 2, ā3) is

A:Ā Click to see the answer

Q:Ā Find the vector of length 2 making an angle of 45Ā° with the x-axis.

A:Ā Find the vector from the given data

Q:Ā he vector as a

A:Ā Click to see the answer

Q:Ā When do line segments directed in the plane represent the same vector

A:Ā Directed Line segments: Partitions occur on line segments are referred as directed segments andā¦

Q:Ā 1- Find the direction of the vector with initial point P(-3,4,1) and terminal point Q(-5,2,2).

A:Ā Since you have asked multiple question, we will solve the first question for you. If you want anyā¦

Q:Ā Find the vector equation of the line through the points P0(x0, y0, z0)Ā and P1(x1, y1, z1).

A:Ā P0x0,Ā y0,Ā z0Ā &Ā P1x1,Ā y1,Ā z1. Now let aāĀ &Ā bā be the position vectors of the points P0x0,Ā y0,ā¦

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