Answer:
Answer is x = -24/13, y = 3/13
Step-by-step explanation:
The vector equation of line is;
(x,y) = ([tex]x_{0},y_{0}[/tex]) + t (v) ............... 1
we know that;
([tex]x_{0},y_{0}[/tex]) = (2,1)
and
v = 5i + 1j
put in equation 1
[tex](x,y) = (2,1) + t (5i + 1j)[/tex]
The parametric equation becomes;
[tex](x,y) = 2i + 1j + 5ti + 1tj[/tex]
by comparison we get;
[tex]x = 5t + 2.................... 2\\y = t + 1................... 3[/tex]
multiply equation 3 by -5 and add it to equation 2
[tex]-5y = -5t - 5\\x = 5t + 2\\\\x - 5y = -3[/tex]
we know that;
[tex]m =(y_2 - y_1)/(x_2 -x_1)[/tex]
so, m = 5
we can find the family of lines that are perpendicular to the above line by swapping the coefficients and change the sign of one of them:
[tex]5x + y = c\\\\where \\x = 3 \\y = 6\\so,\\5(3) + 6 = c\\15 +6 =c\\21=c[/tex]
So, the equation of other line is
[tex]5x+y=21.......4\\x-5y = -3......5\\[/tex]
multiply equation 5 by -5
[tex]-5x+25y=-15\\5x+y=21\\\\26y=6\\y=6/26\\y=3/13[/tex]
put this value of y in equation 5.
[tex]x-5(3/13) =-3\\x-15/13=-3\\x=-3+\frac{15}{13}\\ x=\frac{-24}{13}[/tex]
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