# Math - explanation

posted by .

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)

• Math - explanation -

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

• Math - explanation -

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)

• Math - explanation -

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)

## Similar Questions

1. ### Math: Vectors - Collinear

Can you please check whether my answers are correct?
2. ### Math

Given two non-collinear vectors a and b, show that a, axb, and (axb)xa are mutually perpendicular. Also Express the unit vectors i, j, and k as ordered triplets and show that i x j = k what are ordered triplets?
3. ### Math

Three points D, E, and F are collinear. Is there only one plane that contains these three points?
4. ### math

Are three collinear points are always also coplanar points.
5. ### Mamthematics - Vectors

a) If vector u and vector v are non-collinear vectors show that vector u, vector u cross product vector v and (vector u cross product vector v) cross product vector u are mutually othogonal. b) Verify this property using vectors collinear …
6. ### math

There are nine points on a piece of paper. No three of the points are collinear. How many different triangles can be formed by using three of the nine points as vertices?
7. ### geometry

Please help me to draw this figure four points that are not collinear,three points that are non-collinear,two points that are non-collinear,three points that are non-coplanar,a line containing A and X, three collinear points X,Y,Z, …
8. ### math

My son has been given the collinear problem below that has be stumped two folds. 1- By trying to solve the problem using (y2-y1)/(x2-x1)=slope -- and then, find the (b) in y=mx+b for two points takes way way too long to be a 7th grade …
9. ### Math

Rewrite the following definition as a biconditional: Points that lie on the same line are collinear. A.) If a point lies on a line, then it is collinear. B.) If a point lies on a line with another point, then the two points are collinear. …
10. ### math

Points​ A, B,​ C, D, and E are coplanar and no three are collinear. In how many ways can the plane be named using only these​ points?

More Similar Questions

Post a New Question