AP EAMCET · Maths · Vector Algebra
If \([\mathbf{a} \mathbf{b} \mathbf{c}]=3\), then the volume (in cubic units) of the parallelopiped with \(2 \mathbf{a}+\mathbf{b}, 2 \mathbf{b}+\mathbf{c}\) and \(2 \mathbf{c}+\mathbf{a}\) as edges, is
- A \(15\)
- B \(22\)
- C \(25\)
- D \(27\)
Answer & Solution
Correct Answer
(D) \(27\)
Step-by-step Solution
Detailed explanation
Given that, \[ \text { [abc] }=3 \] Volume of the parallelopiped \[ =[2 \mathbf{a}+\mathbf{b} \mathbf{2} \mathbf{b}+\mathbf{c}+2 \mathbf{c}+\mathbf{a}] \]…
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 \(\cos \alpha+4 \cos \beta+9 \cos \gamma=0\) and \(\sin \alpha+4 \sin \beta+9 \sin \gamma=0\), then \(81 \cos (2 \gamma-2 \alpha)-16 \cos (2 \beta-2 \alpha)=\)AP EAMCET 2024 Hard
- If \(z, i z\) and \(z+i z\) are the vertices of a triangle and if \(|z|=4\), then the area (in sq. units) of that triangle, isAP EAMCET 2017 Hard
- A line \(L\) passes through the point \(P(1,2)\) and makes an angle of \(60^{\circ}\) with \(\overrightarrow{O X}\) in the positive direction. \(A\) and \(B\) are two points lying on \(L\) at a distance of 4 units from P. If 0 is the origin, then the area of \(\triangle 0 \mathrm{AB}\) isAP EAMCET 2025 Medium
- The distance between a point \(P\) whose position vector is \(5 \hat{i}+\hat{j}+3 \hat{k}\) and the line \(\mathbf{r}=(3 \hat{i}+7 \hat{j}+\hat{k})+t(\hat{j}+\hat{k})\) isAP EAMCET 2022 Medium
- Let \(l_1\) be the line passing through the point \(3 \bar{i}+4 \bar{j}-2 \bar{k}\) and parallel to the vector \(-\bar{i}+2 \bar{j}+\bar{k}\). Let \(l_2\) be another line passing through the point \(\bar{i}-7 \bar{j}-2 \bar{k}\) and parallel to the vector \(\bar{i}+3 \bar{j}+2 \bar{k}\). Then the shortest distance between the lines \(l_1\) and \(l_2\) isAP EAMCET 2018 Medium
- The value of '' for which the equation represents a pair of straight lines, isAP EAMCET 2021 Easy
More PYQs from AP EAMCET
- \(20 \mathrm{~mL}\) of \(0.1 \mathrm{M}\) acetic acid is mixed with \(50 \mathrm{~mL}\) of potassium acetate. \(K_a\) of acetic acid \(=1.8 \times 10^{-5}\) at \(27^{\circ} \mathrm{C}\). Calculate concentration of potassium acetate if \(\mathrm{pH}\) of the mixture is 4.8 .AP EAMCET 2009 Hard
- Consider the following cell reaction
\(2 \mathrm{Fe}^{3+}(\mathrm{aq})+2 \mathrm{I}^{-}(\mathrm{aq}) \rightleftharpoons 2 \mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{I}_2(\mathrm{~s})\)
At 298 K, the cell emf is 0.237 V. The equilibrium constant for the reaction is \(10^x\). The value of \(x\) is
\(\left(\mathrm{F}=96500 \mathrm{C} \mathrm{~mol}^{-1} ; \mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)\)AP EAMCET 2025 Medium - If \(x \in R\), then the range of \(\frac{x}{x^2-5 x+9}\) isAP EAMCET 2019 Easy
- Let \((a-3) x^2+12 x+(a+6)>0, \forall x \in R ~\&~ a \in(\ell, \infty)\). If \(\alpha\) is the least positive integral value of \(a\), then the roots of \((\alpha-3) x^2+12 x+(\ell+2)=0\) areAP EAMCET 2025 Medium
- In a triangle \(\mathrm{ABC}\), if \(\tan \left(\frac{A-B}{2}\right)=\frac{1}{3} \tan \left(\frac{A+B}{2}\right)\) then \(a: b=\)AP EAMCET 2017 Medium
- In , suppose the radius of the circle opposite to angle and is denoted by , and . If and is the radius of the circumcircle, then the value ofAP EAMCET 2021 Medium