Example 27 : We have the points A(-2,-3) B(2,-1) C(1,2) D(-1,1)
A) See if AB _|_ BC = AB * BC = 0
AB= [4,2]
BC = [-1,3]
AB * BC = 4 * (-1) + 2 *3 = 2
Since AB * BC is not 0 we know is not AB _|_ BC,
B) Calculate <D) Is made of the vectors DA and DC
DA = [-1,-4] DC = [2,1]
Cos <(DA,DC) = DA * DC/ |[DA]| * |[DC]| = -6/squareroot 17 * squareroot 15
That gives <D = 130,6 degrees,
C) Find the cordinates to the midtpoint on BC
We call the point M and find the vector from origo to M : OM = OB + 1/2 BC = [3/2,1/2]
d) Find the parameter representation for the line going through B and C
Calculate when this line cuts through the Y-axis.
The directon vector for the line is BC = [-1,3] if we choose B [2,-1] as a startpoint the parameter representation will become: X = 2-t and Y= -1 + 3t
The line cuts through the Y-axis when X= 0. We get 2-t=0,that will say t=2.
Then Y=-1 + 3t= -1+3*2=5 the point is [0,5].
Task 2.41
We continue to calculate on example 27
Calculate AD, |AD|, and <A
AD = [-1 - (-2), 1 - (-3)] = [1,4]
|AD| = |[AD]| = squareroot 1^2 + 4^2 = squareroot 1 + 16 = squareroot 17 = 4.123
<A is made of the Vectors AD and AC (or AA and AB, but since i am not sure i choose AD and AC).
AD= [1,4]
AC = [3,5]
cos<(AD, AC) AD = [-1-(-2).1-(-3)]=[1.4] AC=[1-(-2).2-(-3)]=[3.5] cos<AD.AC==[AD]*[AC]/|[AD]|*|[AC]|= 1*3+3*5/1^2+4^2*3^2+5^2= 20 +3/sqrt 1+16 * sqrt 9 + 10 = 23/sqrt 17 * sqrt 19 = 23/4.123*4.358 =23/17.968=23/18= incoverse 1.2777777778 But you can't incoverse that, from here i dont know what to do, to continue the task.
B) See if the quadrilateral is a trapezium
C) Choose E on the x-axis so that AE _|_ AB
D) The point F has the cordinates F (100,4.
Does A,B and F lay on the line?
E) Find the parameter representation for the line through A and D. Choose s like a parameter (s either stands for seconds or velocity on norwegian).
Calculate where this line cuts through the x-axis.
F) Where in the line through A and D does it cut through line B and C?
And i had to give my math book to the library so since i don't have the book aviable (an other person borrowed it) i don't have the answers.
A) See if AB _|_ BC = AB * BC = 0
AB= [4,2]
BC = [-1,3]
AB * BC = 4 * (-1) + 2 *3 = 2
Since AB * BC is not 0 we know is not AB _|_ BC,
B) Calculate <D) Is made of the vectors DA and DC
DA = [-1,-4] DC = [2,1]
Cos <(DA,DC) = DA * DC/ |[DA]| * |[DC]| = -6/squareroot 17 * squareroot 15
That gives <D = 130,6 degrees,
C) Find the cordinates to the midtpoint on BC
We call the point M and find the vector from origo to M : OM = OB + 1/2 BC = [3/2,1/2]
d) Find the parameter representation for the line going through B and C
Calculate when this line cuts through the Y-axis.
The directon vector for the line is BC = [-1,3] if we choose B [2,-1] as a startpoint the parameter representation will become: X = 2-t and Y= -1 + 3t
The line cuts through the Y-axis when X= 0. We get 2-t=0,that will say t=2.
Then Y=-1 + 3t= -1+3*2=5 the point is [0,5].
Task 2.41
We continue to calculate on example 27
Calculate AD, |AD|, and <A
AD = [-1 - (-2), 1 - (-3)] = [1,4]
|AD| = |[AD]| = squareroot 1^2 + 4^2 = squareroot 1 + 16 = squareroot 17 = 4.123
<A is made of the Vectors AD and AC (or AA and AB, but since i am not sure i choose AD and AC).
AD= [1,4]
AC = [3,5]
cos<(AD, AC) AD = [-1-(-2).1-(-3)]=[1.4] AC=[1-(-2).2-(-3)]=[3.5] cos<AD.AC==[AD]*[AC]/|[AD]|*|[AC]|= 1*3+3*5/1^2+4^2*3^2+5^2= 20 +3/sqrt 1+16 * sqrt 9 + 10 = 23/sqrt 17 * sqrt 19 = 23/4.123*4.358 =23/17.968=23/18= incoverse 1.2777777778 But you can't incoverse that, from here i dont know what to do, to continue the task.
B) See if the quadrilateral is a trapezium
C) Choose E on the x-axis so that AE _|_ AB
D) The point F has the cordinates F (100,4.
Does A,B and F lay on the line?
E) Find the parameter representation for the line through A and D. Choose s like a parameter (s either stands for seconds or velocity on norwegian).
Calculate where this line cuts through the x-axis.
F) Where in the line through A and D does it cut through line B and C?
And i had to give my math book to the library so since i don't have the book aviable (an other person borrowed it) i don't have the answers.
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