given-eq-of-line-1-x-y-3-2-t-4-5-2-x-y-1-1-s-7-k-find-t-and-s-if-1-2-if-1-2-

Question Number 92301 by jagoll last updated on 06/May/20

given eq of line

(1) [x, y] = [3, - 2] + t [4, - 5]

(2) [x, y] = [1, 1] + s [7, k]

find t and s if (1) ∥ (2)

if (1) ⊥ (2)

Commented by jagoll last updated on 06/May/20

thank you both

Commented by john santu last updated on 06/May/20

line (1) x = 3 + 4 t \Rightarrow t = \frac{x - 3}{4}

y = - 2 - 5 t \Rightarrow t = \frac{- 2 - y}{5}

\Rightarrow \frac{x - 3}{4} = \frac{- 2 - y}{5}

5 x + 4 y - 7 = 0

line (2) x = 1 + 7 s \Rightarrow s = \frac{x - 1}{7}

y = 1 + s k \Rightarrow s = \frac{y - 1}{k}

\Rightarrow \frac{x - 1}{7} = \frac{y - 1}{k}

k x - 7 y + 7 - k = 0

if parallel \Rightarrow \frac{- 5}{4} = \frac{- k}{- 7}

k = - \frac{35}{4}

if perpendicular \Rightarrow \frac{4}{5} = \frac{k}{7}

k = \frac{28}{5}

Answered by mr W last updated on 06/May/20

(1) / / (2) :

\frac{- 5}{4} = \frac{k}{7}

\Rightarrow k = - \frac{35}{4}

(1) ⊥ (2) :

\frac{- 5}{4} \times \frac{k}{7} = - 1

\Rightarrow k = \frac{28}{5}

p l e a s e c h e c k q u e s t i o n : t a n d s a r e

p a r a m e t e r s a n d a r e o f a n y v a l u e s .

i t i s t o f i n d k = ?

Commented by jagoll last updated on 06/May/20

yes, t & s are parameters sir

Commented by mr W last updated on 06/May/20

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