if-plane-3x-4y-tz-2-and-kx-6y-5z-2-0-are-parallel-find-the-value-of-k-and-t-

Question Number 95779 by i jagooll last updated on 27/May/20

if plane 3 x + 4 y + tz = 2 and

kx + 6 y + 5 z - 2 = 0 are parallel .

find the value of k and t

Answered by john santu last updated on 27/May/20

\frac{3}{k} = \frac{4}{6} = \frac{t}{5}

{\begin{cases} k = \frac{18}{4} = \frac{9}{2} \\ t = \frac{20}{6} = \frac{10}{3} \end{cases}

Commented by i jagooll last updated on 27/May/20

thank you

Answered by Rio Michael last updated on 28/May/20

normal for plane 1 n_{1} = 3 i + 4 j + t k

normal for plane 2 n_{2} = k i + 6 j + 5 k

for parrallel vectors \vec{a} and \vec{b}, \vec{a} = h \vec{b} where h is a constant h \in R

\Rightarrow (3 i + 4 j + t k) = h (k i + 6 j + 5 k)

\Rightarrow 4 = 6 h \Leftrightarrow h = \frac{2}{3}

also 3 = h k \Rightarrow k = \frac{3}{h} = 3 \times \frac{3}{2}, k = \frac{9}{2}

and t = 5 h \Rightarrow t = \frac{10}{3}