A equation for a given straight line is r = (i + 3 j ) + lambda (-i - j ). Show

Question

A equation for a given straight line is r = (i + 3 j ) + lambda (-i - j ). Show that the point (1, 2) does not lie on this line. Construct a equation for the line that does go through the point (1, 2), and is perpendicular to r . Determine the point of intersection of the two lines. You have been assigned the task of breaking a recently intercepted coded message. The efficient running of a battle requires secure communications. It has been discovered that the radio communications used by the enemy has been coded. Just such a coded message has been intercepted and it reads as follows: -14, 10, 5, 9, -8, 14, 23, -35, 20, 13, -6, 5, 21, -8, 5, 5, 8, 5, -5, 1, 9. A chance finding in a document captured from the enemy reveals what you think may be the coding matrix that generated this message. Unfortunately you have two to choose from, namely A = , B = . Your task: Interrogation of some recent prisoners leads you to believe that one of the words in the coded message you have been asked to decode refers to a bitter fruit. What is the entire message? You will find the additional notes on a simple coding exercise helpful here. [Hint: T=20] Notes on coding An example of a simple encoding and decoding problems. Beginning with the message that needs to be sent such an "one is the answer" we construct a single string with out spaces, and position the string into equal length pieces, each piece used as a column of a matrix. In this example we get K = We now use an encoding matrix E, to generate the encoded message C EK = C If E = then C = = and hence the message to be sent is 25 -1 10 r 35 1 9 -3 37 -13 31 4 19 13. We now use a map that replaces the letter with number. In this case I'm going to use A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 25 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 so that we have K = Decoding this message would simply involve constructing C from the received message calculating K with the aid of E-1 and then returning the mapping. This implies that the encoding matrix E is known and that the letter to number mapping R known (or may be guessed).

Explanation / Answer

r = (i + 3j) + (-i -j)..

1.

a)Let r=xi + yj..

if point (1,2) lies on the line then 1- =1 and 3-=2..

which is not supported by so point (1,2) not lies on the given line..

b)Let r1 be the required vector so (r1-(i+2j)).r=0.

Let r1=xi+yj;

so (1-)x +(3-)y =1.(1-)+2.(3-) =7-3.

this is the required equation..

c)

we can find intersection point directly by using normal process of equations

like puting x=1-,y=3- values in the b equation

so it becomes (1-)^2+(3-)^2 =7-3

by solving we will get the intersection point..

2)question is not clear to understand .....

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