Question

Find the point of intersection of the following two lines

r 1 (t)=⟨−36,−9,−9⟩+t⟨−13,−3,−2⟩
r2 (t)=⟨−1,0,1⟩+s⟨12,3,3⟩
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Answer 1

To find the point of intersection of the two lines, set the equations equal to each other and solve for the values of t and s. The point of intersection is (1, 1/4, 1/4).

Step-by-step explanation:

To find the point of intersection of the two lines, we need to set the two equations equal to each other and solve for the values of t and s. The equation is:

-36 - 13t = -1 + 12s

To solve this equation, we can rearrange it to:

-36 + 1 = 12s - 13t

-35 = 12s - 13t

Now, we have a system of equations that we can solve simultaneously:

solve the equation -35 = 12s - 13t
with respect to s

12s = 13t - 35

s = (13t - 35)/12

Now, substitute this value of s into one of the original equations and solve for t:

-36 - 13t = -1 + 12((13t - 35)/12)

-36 - 13t = -1 + 13t - 35

-36 = -36t

t = 1

Substitute t = 1 back into the equation for s to find its value:

s = (13(1) - 35)/12

s = 3/12

s = 1/4

Therefore, the point of intersection of the two lines is (1, 1/4, 1/4).