Download App

Three Dimensional Geometry — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsThree Dimensional Geometry3 Marks
Question
If the lines $\frac{\text{x}-1}{-3}=\frac{\text{y}-2}{2\text{k}}=\frac{\text{z}-3}{2}\ \text{and}\ \frac{\text{x}-1}{3\text{k}}=\frac{\text{y}-1}{1}=\frac{\text{z}-6}{-5}$ are perpendicular, find the value of k.
✓

Answer

The given lines are
$\frac{\text{x}-1}{-3}=\frac{\text{y}-2}{2\text{k}}=\frac{\text{z}-3}{3}$
and $\frac{\text{x}-1}{3\text{k}}=\frac{\text{y}-1}{1}=\frac{\text{z}-6}{-5}$
Direction ratios of two lines are -3, 2k, 2 and 3k, 1, -5
Since the lines are perpendicular
$\therefore$ (-3)(3k) + (2k)(1) + (2)(-5) = 0
$\therefore$ -9k + 2k - 10 = 0
⇒ -7k = 10
$\therefore\ \text{k}=-\frac{10}{7}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Three Dimensional Geometry→Three Dimensional Geometry — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find fog and gof if:$f(x) = x + 1, g(x) = e^x$
→
Let $f : R \rightarrow R$ be the function defined by $f(x) = 2x – 3 ∀ x \in R$. write $ f^{-1}.$
→
Discuss the continuity of the following functions at the indicated point:
$\text{f}\text{(x)}=\begin{cases}\frac{\text{|x}^2-1|}{\text{x}-1},\text{for} & \text{x} \neq1\\2, &\text{for} \text{ x} = 1\end{cases} \text{at x}=1$
→
If $\text{f(x)}=\sqrt{\text{x}+3}$ and $g(x) = x^2 + 1$ be two real functions, then find fog and gof.
→
If $\text{f(x)}=\begin{cases}2\text{x}^2+\text{k},&\text{if }\text{ x}\geq0\\-2\text{x}^2+\text{k},&\text{if }\text{ x}<0\end{cases},$ then what should be the value of k so that f(x) is continuous at x = 0.
→
If $\text{y}=\text{x}\sin\text{y},$ prove that $\frac{\text{dx}}{\text{dx}}=\frac{\sin^2\text{y}}{(1-\text{x}\cos\text{y})}$
→
Solve the following differential equation
$\frac{\text{dy}}{\text{dx}}=\sin^2\text{y}$
→
Find the inverse of $5$ under multiplication modulo $11$ on $Z_{11}.$
→
Find $A^2 - 5A + 6I$ if A = $\begin{bmatrix}2&0&1\\2&1&3\\1&-1&0\end{bmatrix}.$
→
Find $\lambda$ when the projection of $\vec{\text{a}}=\lambda\hat{\text{i}}+\hat{\text{j}}+4\hat{\text{k}}$ on $\vec{\text{b}}=2\hat{\text{i}}+6\hat{\text{j}}+3\hat{\text{k}}$ is 4 units.
→