If the lines x - 1- - 3 - y - 2- 2k - z - 3- 2 and x - 1-3k - y - 2- 1 - z - 3- - 5 are perpendicular- Find the value of k-

[ x 1 / 3 = y 2 / 2k = z 3 / 2 and x 1 / 3k = y 2 / 1 = z 3 / 5 #160;; ...

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Byju's Answer

Standard XII

Mathematics

Distance between Two Parallel Planes

If the lines ...

Question

If the lines $\frac{x - 1}{- 3} = \frac{y - 2}{2 k} = \frac{z - 3}{2}$ and $\frac{x - 1}{3 k} = \frac{y - 2}{1} = \frac{z - 3}{- 5}$ are perpendicular. Find the value of k.

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Solution

$\begin{matrix} \frac{x - 1}{- 3} = \frac{y - 2}{2 k} = \frac{z - 3}{2} a n d \frac{x - 1}{3 k} = \frac{y - 2}{1} = \frac{z - 3}{- 5} \to b = - 3 ˆ i + 2 k ˆ j + 2 ˆ k \to b^{^{'}} = 3 k ˆ i + ˆ j - 5 ˆ k \to b . \to b^{^{'}} = 0 - 9 k + 2 k - 10 = 0 - 7 k = 10 k = \frac{- 10}{7} \end{matrix}$
Hence, the value of $k$ is $- 10 / 7$ .

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Similar questions

Q. If the lines

\frac{x - 1}{- 3} = \frac{y - 2}{2 k} = \frac{z - 3}{2}

and

\frac{x - 1}{3 k} = \frac{y - 1}{1} = \frac{z - 6}{- 5}

are perpendicular, find the value of

k

If the lines $\frac{x - 1}{- 3} = \frac{y - 2}{2 k} = \frac{z - 3}{2} a n d \frac{x - 1}{3 k} = \frac{y - 1}{1} = \frac{z - 6}{- 5}$ perpendicular, then find the value of k.

Q. If the line

\frac{x - 1}{- 3} = \frac{y - 2}{2 k} = \frac{z - 3}{2}

and

\frac{x - 1}{3 k} = \frac{y - 5}{1} = \frac{z - 6}{- 5}

are perpendicular to each other then

k =

Q. The value of

k

so that the lines

\frac{x - 1}{- 3} = \frac{y - 2}{2 k} = \frac{z - 3}{2}

\frac{x - 1}{3 k} = \frac{y - 5}{1} = \frac{z - 6}{- 5}

are perpendicular to each other, is:

Q. The value of

k

for which the lines

\frac{x + 1}{- 3} = \frac{y + 2}{2 k} = \frac{z - 3}{2} and \frac{x - 1}{3 k} = \frac{y + 5}{1} = \frac{z + 6}{7}

may be perpendicular is:

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If the lines x−1−3=y−22k=z−32 and x−13k=y−21=z−3−5 are perpendicular. Find the value of k.

x−1−3=y−22k=z−32andx−13k=y−21=z−3−5→b=−3ˆi+2kˆj+2ˆk→b′=3kˆi+ˆj−5ˆk→b.→b′=0−9k+2k−10=0−7k=10k=−107Hence, the value of k is −10/7.

If the lines $\frac{x - 1}{- 3} = \frac{y - 2}{2 k} = \frac{z - 3}{2}$ and $\frac{x - 1}{3 k} = \frac{y - 2}{1} = \frac{z - 3}{- 5}$ are perpendicular. Find the value of k.