The shortest distance between the lines x - 3 3 = y - 8 - 1 = z - 3 1 and x + 3 - 3 = y + 7 2 = z - 6 4 is

w → = i ^ + j ^ – 3 k ^ p → = 3 i ^ - j ^ + k ^ q → = - 3 i ^ + 2 j ^ + 4 k ^ p → × q → = i j k 3 - 1 1 - 3 2 4 = 6 i ^ - 15 j ^ + 3 k ^ S . D . = | A B . p × q | p × q = 36 + 225 + 9 36 + 225 + 9 = 3 30

Home

Mathematics - Vector Question with Solution | TestHub

MathematicsVectorVector equation of a line, Vector equation of the angle bisectorsEasy2 minPYQ_2020

MathematicsEasysingle choice

The shortest distance between the lines $\frac{x - 3}{3} = \frac{y - 8}{- 1} = \frac{z - 3}{1}$ and $\frac{x + 3}{- 3} = \frac{y + 7}{2} = \frac{z - 6}{4}$ is

Options:

Answer:

Solution:

$\vec{w} = \hat{i} + \hat{j} - 3 \hat{k}$
$\vec{p} = 3 \hat{i} - \hat{j} + \hat{k}$
$\vec{q} = - 3 \hat{i} + 2 \hat{j} + 4 \hat{k}$
$\vec{p} \times \vec{q} = |\begin{matrix} i & j & k \\ 3 & - 1 & 1 \\ - 3 & 2 & 4 \end{matrix}| = 6 \hat{i} - 15 \hat{j} + 3 \hat{k}$
$S . D . = \frac{| A B . (p \times q) |}{|p \times q|} = \frac{|36 + 225 + 9|}{\sqrt{36 + 225 + 9}} = 3 \sqrt{30}$

Stream:JEESubject:MathematicsTopic:VectorSubtopic:Vector equation of a line, Vector equation of the angle bisectors

⏱ 2mℹ️ Source: PYQ_2020

Doubts & Discussion

Loading discussions...