MHT CET · Maths · Vector Algebra
The volume of parallelopiped, whose coterminous edges are given by \(\bar{u}=\hat{i}+\hat{j}+\lambda \hat{k}\), \(\bar{v}=\hat{i}+\hat{j}+3 \hat{k}, \bar{w}=2 \hat{i}+\hat{j}+\hat{k}\) is 1 cu. units. If \(\theta\) is the angle between \(\bar{u}\) and \(\bar{w}\), then the value of \(\cos \theta\) is
- A \(\frac{3}{4}\)
- B \(\frac{5}{6}\)
- C \(\frac{1}{5}\)
- D \(\frac{1}{6}\)
Answer & Solution
Correct Answer
(B) \(\frac{5}{6}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Volume of parallelepiped }=\left[\begin{array}{lll}\overrightarrow{\mathrm{u}} & \overrightarrow{\mathrm{v}} & \overrightarrow{\mathrm{w}}\end{array}\right] \\ & \quad\left|\begin{array}{lll}1 & 1 & \lambda \\ 1 & 1 & 3 \\ 2 & 1 & 1\end{array}\right|=1 \\ & \Rightarrow \lambda=2 \\ & \therefore \quad \cos \theta=\frac{2+1+2}{\sqrt{6} \cdot \sqrt{6}}=\frac{5}{6}\end{aligned}\)
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
- \(\lim _{x \rightarrow 0} \frac{9^x-4^x}{x\left(9^x+4^x\right)}=\)MHT CET 2024 Easy
- The locus of the points represented by \(|z+3|-|z-3|=6\), where \(z\) is a complex number, is ....MHT CET 2025 Medium
- If the function \(f(x)\) is continuous on its domain \([-2,2]\) where \(f(x)=\frac{\sin a x}{x}+3,-2 \leq x < 0=x+5,0 \leq x \leq 1,\) \(=\sqrt{x^2+8}-b, 1 < x \leq 2\) then \(7 a+b+1\) is equal toMHT CET 2022 Medium
- \(\hat{a}, \hat{b}\), and \(\hat{c}\) are three unit vectors such that \(\hat{a} \times(\hat{b} \times \hat{c})=\frac{\sqrt{3}}{2}(\hat{b}+\hat{c})\). If \(\vec{b}\) is not parallel to \(\hat{c}\), then the angle between \(\hat{a}\) and \(\hat{b}\) isMHT CET 2024 Medium
- For \(\mathrm{k}=1,2,3\) the box \(\mathrm{B}_{\mathrm{k}}\) contains k red balls and \((\mathrm{k}+1)\) white balls. Let \(\mathrm{P}\left(\mathrm{B}_1\right)=\frac{1}{2}, \mathrm{P}\left(\mathrm{B}_2\right)=\frac{1}{3}\) and \(\mathrm{P}\left(\mathrm{B}_3\right)=\frac{1}{6}\). A box is selected at random and a ball is drawn from it. If a red ball is drawn from it, then the probability that it comes from box \(B_2\) isMHT CET 2025 Medium
- Let \(\bar{a}, \overline{\mathrm{~b}}, \overline{\mathrm{c}}, \overline{\mathrm{d}}\) are vectors such that \(\bar{a} \times \overline{\mathrm{b}}=2 \hat{i}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}\) and \(\overline{\mathrm{c}} \times \overline{\mathrm{d}}=3 \hat{i}+2 \hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}\) and if \(\left|\begin{array}{cc}\bar{a} \cdot \overline{\mathrm{c}} & \overline{\mathrm{b}} \cdot \overline{\mathrm{c}} \\ \bar{a} \cdot \overline{\mathrm{~d}} & \overline{\mathrm{~b}} \cdot \overline{\mathrm{~d}}\end{array}\right|=0\), then \(\lambda=\)MHT CET 2025 Medium
More PYQs from MHT CET
- Which among the following sets of compounds is used as raw material for the preparation of sodium carbonate by Solvay process?MHT CET 2019 Medium
- Given below are the steps involved in plant breeding program. Identify the correct sequence of these steps.
i. collection of variabilities
ii. Hybridization
iii. evaluation and selection of parents
iv. testing, release and commercialization of new cultivars.
v. selection and testing of superior recombinants.MHT CET 2025 Hard - The magnetic induction due to an ideal solenoid is independent ofMHT CET 2024 Easy
- What is the percentage of carbon in urea?MHT CET 2019 Medium
- f a line in octant OXYZ makes equal angles with co-ordinate axes, thenMHT CET 2020 Easy
- Matrix then the value of isMHT CET 2018 Medium