Answer:
The vector is < 91 / sqrt(53),26 / sqrt(53)> or <-91 / sqrt(53),-26 / sqrt(53)>
Explanation:
7x + 2y =6
We need to find the slope so we solve for y
Subtract 7x from each side
7x -7x+ 2y =-7x+6
2y = -7x +6
Divide by 2
2y/2 = -7x /2 + 6/2
y = -7/2 x +3
The slope is -7/2
We want it perpendicular so the slope must be the negative reciprocal
m = -(-2/7)
= 2/7
Vectors are written in the form
v = < x, y>
slope = change in y over change in x
So y/x = 2/7 or 7y =2x
Now we worry about the magnitude
Magnitude is sqrt(x^2 + y^2) and it equals 13
sqrt(x^2 + y^2)= 13
square both sides
x^2 + y^2 = 169
We have 2 equations and 2 unknowns
y = (2/7x)
x^2 +(2/7x) ^2 = 169
x^2 +4/49 x^2 =169
49/49 x^2 +4/49 x^2 = 169
53/49 x^2 = 169
x^2 = 169 *49/53
Take the square root of each side
x = ±91 / sqrt(53)
y = (2/7x)
= 2/7 * ±91 / sqrt(53)
= ±26 / sqrt(53)
The vector is < 91 / sqrt(53),26 / sqrt(53)> or <-91 / sqrt(53),-26 / sqrt(53)>