MHT CET · Maths · Three Dimensional Geometry
If \(P(3,2,6)\) is a point in space and \(Q\) is a point on the line \(\bar{r}=(\hat{i}-\hat{j}+2 \hat{k})+\mu(-3 \hat{i}+\hat{j}+5 \hat{k})\), then the value of \(\mu\) for which the vector \(\overline{P Q}\) is parallel to the plane \(x-4 y+3 z=1\), is
- A \(\frac{1}{4}\)
- B \(-\frac{1}{8}\)
- C \(\frac{1}{8}\)
- D \(-\frac{1}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
\(P \equiv 3 \hat{i}+2 \hat{j}+6 \widehat{k} \text { and } Q \equiv(1-3 \mu) \hat{i}+(\mu-1) \hat{j}\) \(+~(2+5 \mu) \widehat{k}\)
\(\Rightarrow \overrightarrow{P Q}=(-2-3 \mu) \hat{i}+(\mu-3) \hat{j}+(5 \mu-4) \hat{k}\)
\(\because \overrightarrow{P Q}\) is parallel to the plane \(x-4 y+3 z=1\)
\(\Rightarrow \overrightarrow{P Q}=(-2-3 \mu) \hat{i}+(\mu-3) \hat{j}+(5 \mu-4) \hat{k}\)
\(\because \overrightarrow{P Q}\) is parallel to the plane \(x-4 y+3 z=1\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(\mathrm{A}+\mathrm{B}=\left[\begin{array}{cr}1 & \tan \frac{\theta}{2} \\ -\tan \frac{\theta}{2} & 1\end{array}\right]\) where A is symmetric and B is skew-symmetric matrix, then the matrix \(\left(A^{-1} B+A B^{-1}\right)\) at \(\theta=\frac{\pi}{6}\) is given byMHT CET 2024 Hard
- \(\int_{2}^{3} \frac{x}{x^{2}-1} d x=\)MHT CET 2020 Easy
- The general solution of the equation \(\sqrt{3} \cos \theta+\sin \theta=\sqrt{2}\) isMHT CET 2024 Hard
- The magnitude of the projection of the vector \(2 \hat{i}+3 \hat{j}+\hat{k}\) on the vector perpendicular to the plane containing the vectors \(\hat{i}+\hat{j}+\hat{k}\) and \(\hat{i}+2 \hat{j}+3 \hat{k}\) isMHT CET 2022 Medium
- In 3-dimensional space, the equation \(x^2-8 x+12=0\) represents ....MHT CET 2025 Easy
- The value of \(\int \frac{\mathrm{d} x}{7+6 x-x^2}\) is equal toMHT CET 2024 Hard
More PYQs from MHT CET
- Weak acid HX has dissociation constant \(1 \times 10^{-5}\). Calculate the percent dissociation in its \(0.1 \mathrm{M}\) solution.MHT CET 2023 Medium
- Let \(\mathrm{f}:[-1,3] \rightarrow \mathbb{R}\) be defined as
\(|x|+[x], -1 \leqslant x \lt 1 \ x+|x|, 1 \leqslant x \lt 2 \ x+[x],\) \(2 \leqslant x \leqslant 3\)
where \([t]\) denotes the greatest integer function.
Then f is discontinuous atMHT CET 2024 Hard - Calculate the solubility product of sparingly soluble salt BA at 300 K if its solubility is \(9.1 \times 10^{-3} \mathrm{moldm}^{-3}\) at same temperature.MHT CET 2024 Medium
- If the temperature of cold junction of thermocouple is lowered, then the neutral temperatureMHT CET 2008 Easy
- The angle between the lines whose direction cosines are \(\frac{-\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\) and \(\frac{-\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\) isMHT CET 2025 Easy
- An air column in a closed organ pipe vibrating in unison with a fork, produces second overtone. The vibrating air column hasMHT CET 2024 Medium