MHT CET · Maths · Vector Algebra
The direction ratios of the line perpendicular to the lines having direction ratios \(2,3,1\)
and \(1,2,1\) are
- A \(-2,1,1\)
- B \(1,1,1\)
- C \(1,-1,1\)
- D \(2,2,-2\)
Answer & Solution
Correct Answer
(C) \(1,-1,1\)
Step-by-step Solution
Detailed explanation
(D)
Let \(\bar{a}\) and \(\bar{b}\) be the vectors along the lines whose direction ratios are \(2,3,1\) and \(1,2,1\) respectively.
\(\therefore \overline{\mathrm{a}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}} \quad \text { and } \quad \overline{\mathrm{b}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}\)
A vector perpendicular to both \(\bar{a}\) and \(\bar{b}\) is given by,
\(\bar{a} \times \bar{b}=\left|\begin{array}{ccc}
\hat{i} & \hat{j} & \hat{k} \\
2 & 3 & 1 \\
1 & 2 & 1
\end{array}\right|=\hat{i}(3-2)-\hat{j}(2-1)+\hat{k}(4-3)=\hat{i}-\hat{j}+\hat{k}\)
Hence d.r.s are \(1,-1,1\)
Let \(\bar{a}\) and \(\bar{b}\) be the vectors along the lines whose direction ratios are \(2,3,1\) and \(1,2,1\) respectively.
\(\therefore \overline{\mathrm{a}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}} \quad \text { and } \quad \overline{\mathrm{b}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}\)
A vector perpendicular to both \(\bar{a}\) and \(\bar{b}\) is given by,
\(\bar{a} \times \bar{b}=\left|\begin{array}{ccc}
\hat{i} & \hat{j} & \hat{k} \\
2 & 3 & 1 \\
1 & 2 & 1
\end{array}\right|=\hat{i}(3-2)-\hat{j}(2-1)+\hat{k}(4-3)=\hat{i}-\hat{j}+\hat{k}\)
Hence d.r.s are \(1,-1,1\)
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
- The maximum value of \(\mathrm{z}=x+y\), subjected to \(x+y \leq 10,5 x+3 y \geq 15, x \leq 6, x, y \geq 0\)MHT CET 2024 Easy
- If \(\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}\) are three vectors such that \(|\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}}|=1\), \(\overline{\mathrm{c}}=\lambda(\overline{\mathrm{a}} \times \overline{\mathrm{b}})\) and \(|\overline{\mathrm{a}}|=\frac{1}{\sqrt{3}},|\overline{\mathrm{b}}|=\frac{1}{\sqrt{2}},|\overline{\mathrm{c}}|=\frac{1}{\sqrt{6}}\), then the angle between \(\bar{a}\) and \(\bar{b}\) isMHT CET 2023 Hard
- Water at \(100^{\circ} \mathrm{C}\) cools in 10 minutes to \(80^{\circ} \mathrm{C}\) in a room temperature of \(25^{\circ} \mathrm{C}\), then the temperature of water after 20 minutes will beMHT CET 2022 Hard
- From a group of 8 boys and 3 girls, a commitee of 5 members to be formed. Find the probability that 2 particular girls are included in the committe isMHT CET 2009 Hard
- Let the line \(\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}\) lie in the plane \(x+3 y-\alpha z+\beta=0\), then the value of \((\beta-\alpha)\) is equal toMHT CET 2025 Medium
- The L.P.P. to maximize \(z=x+y\), subject to \(x+y \leq 30, x \leq 15, y \leq 20, x+y \geq 15\),
\(x, y \geq 0\) hasMHT CET 2020 Easy
More PYQs from MHT CET
- In the thermodynamic processes, which of the following statements is NOT true?MHT CET 2025 Easy
- Maximum value of \(\mathrm{Z}=100 x+70 y\) Subject to \(2 x \geq 4, y \leq 3, x+y \leq 8, x, y \geq 0\) isMHT CET 2024 Easy
- A line drawn from the point \(\mathrm{A}(1,3,2)\) parallel to the line \(\frac{x}{2}=\frac{y}{4}=\frac{z}{1}\), intersects the plane \(3 x+y+2 z=5\) in point \(\mathrm{B}\), then co-ordinates of point \(\mathrm{B}\) areMHT CET 2023 Medium
- The number of positive integral solutions of \(\tan ^{-1} x+\cos ^{-1}\left(\frac{y}{\sqrt{1+y^2}}\right)=\sin ^{-1}\left(\frac{3}{\sqrt{10}}\right)\) areMHT CET 2025 Medium
- A diatomic molecule has moment of inertia 'I'. By applying Bohr's quantization condition, its rotational energy in the \(\mathrm{n}^{\text {th }}\) level is \([\mathrm{n} \geq 1]\) [h= Planck's constant \(]\)MHT CET 2024 Medium
- What is IUPAC name of acrolein?MHT CET 2020 Medium