Which value of k will make the lines parallel
r= (1,2)+s(2,3), S e R and 12x + ky=0
the slope of 12x + ky = 0 is -12/k
the slope of the vector equation is 3/2
-12/k = 3/2
3k = -24
k = -8
To determine the value of k that will make the lines parallel, we need to compare their slopes.
The given equation of a line in vector form is r = (1,2) + s(2,3), where s is a parameter. We can rewrite this equation in slope-intercept form by converting the vector form into scalar form:
r = (1,2) + s(2,3)
r = (1 + 2s, 2 + 3s)
From here, we can conclude that the slope of this line is 3.
The equation of the second line is 12x + ky = 0. To find its slope-intercept form, we can solve for y:
ky = -12x
y = -12x/k
Now we can see that the slope of this line is -12/k.
For the lines to be parallel, their slopes must be equal. So we can set up an equation:
3 = -12/k
Now we can solve for k:
3k = -12
k = -12/3
k = -4
Therefore, the value of k that will make the lines parallel is -4.
To determine which value of k will make the lines parallel, we need to compare the slopes of the two lines.
The line represented by the equation r = (1, 2) + s(2, 3) has a direction vector of (2, 3).
The line represented by the equation 12x + ky = 0 is in the form y = -(12/k)x, where the slope is -12/k.
If two lines are parallel, their slopes must be equal.
Therefore, we need to find the value of k that makes the slope of the second line (-12/k) equal to the slope of the first line (which is 3/2).
To find this value, we set -12/k = 3/2 and solve for k:
-12/k = 3/2
To get rid of the fractions, we can multiply both sides of the equation by 2k:
-24 = 3k
Divide both sides by 3:
-8 = k
Therefore, the value of k that will make the lines parallel is k = -8.