Math - explanation

This is an example in the text book.

Using vectors, demonstrate that the three points A(5, -1), B(-3,4) and C(13,-6) are collinear.

Solution
AB = (-8, 5)
BC = (16, -10)
Then BC = 2AB

AB and BC have the opposite direction, so the points A, B, and C must be collinear.

I don't understand how AB = (-8, 5) and
BC = (16, -10)

asked by Anonymous
  1. vector AB is (-3 -5) i + (4 - (-1) ) j
    = -8 i + 5 j

    vector BC is (13 - (-3)) i + (-6 - 4) j
    = 16 i - 10 j

    posted by Damon
  2. Now the lines are collinear because they go through the same point (point B)
    and they have the same slope (although one is going down the hill while the other goes up)

    posted by Damon
  3. I'm not sur if this will help, but to get AB, you subtract A from B and B from C.

    B(-3x,4y)-A(5x,-1y)=x(-3-5),y(4+1)=
    AB(-8,5)

    C(13x,-6y)-B(-3x,4y)=x(13+3),y(-6-4)=
    BC(16,-10)

    posted by Amanda

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math: Vectors - Collinear

    Can you please check whether my answers are correct? If they aren't, how would you find if the points are parallel to one another with 3 coordinates? Using vectors, demonstrate that these points are collinear. a) P(15 , 10) Q(6 ,
  2. Faculty of Business Studies

    LB160 TMA01 • This TMA01 contains 3 parts. Student should answer either Part 1 or Part 2. Part 3 is compulsory. • The value of TMA01 is 15 points. • The mark assigned to each part is 7.5 points.
  3. English

    Hi! Need some advice.Next week I need to teach a class. My task is to find a text (I have found it,it's a german literature)and now I need to do something with this text and it needs to last for 45-60 minutes.It shouldn't be just
  4. physics

    Consider the directions of the velocity and the acceleration vectors of an object in uniform circular motion. A. Both vectors point away from the center. B. The velocity points along the tangent, and the acceleration is zero,
  5. Physics

    1) The vector sum of three vectors gives a resultant equal to zero. what can you say about the vectors? 2) Vector is 3.00 units in length and points along the positive x-axis. Vector is 4.00 units in length and points along the
  6. Science

    1) The vector sum of three vectors gives a resultant equal to zero. what can you say about the vectors? 2) Vector is 3.00 units in length and points along the positive x-axis. Vector is 4.00 units in length and points along the
  7. PHYSICS

    Vector A⃗ points in the negative x direction and has a magnitude of 22 units. The vector B⃗ points in the positive y direction. partA:Find the magnitude of B⃗ if A⃗ +B⃗ has a magnitude of 37 units. partB: Sketch A⃗ and
  8. Language Arts

    I left my McMillian text book for language arts in school today and I have homework on page 2 and 3. I'm in the 6th grade does anyone have that book. I really really need those questions. I don't know if this gives page numbers
  9. 12th grade

    prove that normal to plane containing 3 points whose position vectors are a vector,b vector,c vectorlies in direction addition of cross product of vectors b and c and cross product of vectors c and a and cross product of vectors a
  10. physics

    Vector has a magnitude of 136 units and points 35.0 ° north of west. Vector points 69.0 ° east of north. Vector points 19.0 ° west of south. These three vectors add to give a resultant vector that is zero. Using components,

More Similar Questions