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Dvinal [7]
3 years ago
8

Consider the following.

Mathematics
1 answer:
Fantom [35]3 years ago
5 0

Answer:

(-8, 7); x + y = 13 → y= -x + 13

parallel lines have the same slope. slope is -1

y = -x + b

7 = -(-8) + b

7 = 8 + b

b = -1

(a) y = -x - 1

perpendicular lines have opposite slopes. slope is 1/2.

y = -1/2x + b

7 = -1/2(-8) + b

7 = 4 + b

b = 3

(b) y = -1/2x + 3

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Answer:

r(t) and s(t) are parallel.

Step-by-step explanation:

Given that :

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r(t)=⟨1−t,3+2t,−3t⟩

s(t)=⟨2t,−3−4t,3+6t⟩

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NOTE:

Two lines will be parallel if \dfrac{x_1}{x_2}= \dfrac{y_1}{y_2}= \dfrac{z_1}{z_2}

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r(t) = \dfrac{x-1}{-1} = \dfrac{y-3}{2}=\dfrac{z-0}{-3} = t

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s(t) = \dfrac{x-0}{2} = \dfrac{y+5}{-4}=\dfrac{z-3}{6} = t

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\dfrac{d_1}{d_2}= \dfrac{-1}{2} = \dfrac{2}{-4}= \dfrac{-3}{-6}

Hence, we can conclude that r(t) and s(t) are parallel.

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