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 , 4)
R(12 , 8)
Vector PQ = (9 , 6)
Vector QR = (18 , 12)
Vector RP = (27 , 18)
(9 / 27 / 18) = (6 / 18 / 12)
Therefore, not collinear.
b)
D(33, 5, 20)
E(6, 4, 16)
F(9, 3, 12)
Vector DE = (27, 9, 36)
Vector EF = (3, 1, 4)
Vector FD = (24, 8, 7)
(27 / 3 / 24) = (9 /  1 / 8) = (36 / 4 / 7)
Therefore, not collinear.

no
Vector PQ = (9 , 6)
Vector QR = (18 , 12)
so vector QR = 2(9,6) = 2PQ
so P,Q and R are collinear since we were able to express them as a linear combination.
same thing in b)
notice that (27,9,36) = 9(3,1,4)posted by Reiny

zhsicfn rcpeqd tfnvchzbo ohymq rsgvzqwyk jkwgaf atdvcm
posted by kmseaw fbnop
Respond to this Question
Similar Questions

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 
math
My son has been given the collinear problem below that has be stumped two folds. 1 By trying to solve the problem using (y2y1)/(x2x1)=slope  and then, find the (b) in y=mx+b for two points takes way way too long to be a 7th 
geometry
Please help me to draw this figure four points that are not collinear,three points that are noncollinear,two points that are noncollinear,three points that are noncoplanar,a line containing A and X, three collinear points 
Math  Equations of plane(check)
Consider the plane that contains points A(2,3,1), B(11,1,2), C(7,3,6). a) Find two vectors that are parallel to the plane. Ans: AC, BC or AB will be parallel to the plane. b) Find two vectors that are perpendicular to the 
Math  Equations of plane(check)
Consider the plane that contains points A(2,3,1), B(11,1,2), C(7,3,6). a) Find two vectors that are parallel to the plane. Ans: AC, BC or AB will be parallel to the plane. b) Find two vectors that are perpendicular to the 
math
In a reference (O, i, j), the points A (12, 1150) and B (10, 500). The function f is defined on (20, 10) by: f(x) = x^ 4 +2.25 x^344.5x^2260x+100 We note Cf his(her,its) representative curve. We try to determine all the 
maths
In a reference (O, i, j), the points A (12, 1150) and B (10, 500). The function f is defined on (20, 10) by: f(x) = x^ 4 +2.25 x^344.5x^2260x+100 We note Cf his(her,its) representative curve. We try to determine all the 
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 
Vectors/Calc
Note: u,v,w,a,b are all vectors Given that u= xa + 2yb v= 2ya + 3yb w= 4a  2b where a and b are collinear, find the values of x and y for which 2u  v =w 
Mamthematics  Vectors
a) If vector u and vector v are noncollinear 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