Question

C коллинеарный p, p(12;-5) модуль с = 26, найти координаты с

Answer 1

Ответ:     с( 24 ;- 10 ) .  

Объяснение:

Нехай коорд. вектора  с( a ; b ) . Так як вектори с  і  р - колінеарні,

то має місце пропорція :  a/12 = b/(- 5 ) = k . Звідси а = 12k ; b = -5k .

| c | = 26  i  | c | = √ ( a² + b² ) = √[ ( 12k )² + (- 5k )² ] = √(169k²) = 13k .

Отже , 13k = 26 ;  ----> k = 26 : 13 ; ---->  k = 2 , тому a = 24 ;  b = - 10 .

Kоорд. вектора  с( 24 ;- 10 ) .

Answer 2

Finding the Coordinates of Point C

To find the coordinates of point C, we are given that point P (12, -5) is collinear with point C and that the magnitude of vector PC is 26.

To solve this problem, we can use the formula for the magnitude of a vector:

|PC| = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) are the coordinates of point P and (x2, y2) are the coordinates of point C.

Given that |PC| = 26 and P(12, -5), we can substitute these values into the formula and solve for the coordinates of point C.

26 = sqrt((x2 - 12)^2 + (y2 - (-5))^2)

Squaring both sides of the equation, we get:

676 = (x2 - 12)^2 + (y2 + 5)^2

Expanding the equation, we have:

676 = x2^2 - 24x2 + 144 + y2^2 + 10y2 + 25

Combining like terms, we get:

x2^2 + y2^2 - 24x2 + 10y2 + 169 = 0

Now, we can solve this equation to find the coordinates of point C. However, it seems that the given information is incomplete or there might be an error in the problem statement, as there are no further details or constraints provided to determine the specific coordinates of point C.

Please provide additional information or constraints so that we can accurately determine the coordinates of point C.