AP EAMCET · Maths · Vector Algebra
The area of the parallelogram for which the vectors \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) are adjacent sides is equal to
- A \(3 \sqrt{5}\)
- B \(5 \sqrt{3}\)
- C \(2 \sqrt{5}\)
- D \(5 \sqrt{6}\)
Answer & Solution
Correct Answer
(B) \(5 \sqrt{3}\)
Step-by-step Solution
Detailed explanation
Let \(\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\mathbf{b}=3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) \(\therefore\) Area of parallelogram \(=|\mathbf{a} \times \mathbf{b}|\)…
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 differential equation of the family \(y=a e^x+b x e^x+c x^2 e^x\) of curves, where \(a, b, c\) are arbitrary constants, isAP EAMCET 2009 Easy
- If a function defined by \(f(x)=\frac{\left(3^x-1\right)^2}{\sin x \log (1+x)}, x \neq 0\), is continuous at \(\mathrm{x}=0\), then \(\mathrm{f}(0)=\)AP EAMCET 2023 Medium
- If the curves \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) and \(\frac{x^2}{25}+\frac{y^2}{16}=1\) cut each other orthogonally, then \(a^2-b^2\) equals toAP EAMCET 2014 Medium
- The number of non-trivial solutions of the system
\(x-y+z=0, x+2 y-z=0, \quad 2 x+y+3 z=0\)
isAP EAMCET 2007 Easy - If \(a \sin ^2 \theta+b \cos ^2 \theta=c\), then \(\tan ^2 \theta\) is equal toAP EAMCET 2010 Medium
- One of the complex roots of the equation \(x^{11}-x^6-x^5+1=0\) isAP EAMCET 2018 Medium
More PYQs from AP EAMCET
- \(0.16 \mathrm{~g}\) of an organic compound containing sulphur produces \(0.233 \mathrm{~g}\) of \(\mathrm{BaSO}_4\). Percentage of sulphur in the compound isAP EAMCET 2011 Easy
- The half life of \({ }_{92}^{238} \mathrm{U}\) against \(\alpha\)-decay is \(13.86 \times 10^{16} \mathrm{~s}\). The activity of \(1 \mathrm{~g}\) sample of \({ }_{92}^{238} \mathrm{U}\) isAP EAMCET 2018 Easy
- If \(\mathbf{a}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}, \mathbf{b}=m \hat{\mathbf{i}}+n \hat{\mathbf{j}}+12 \hat{\mathbf{k}}\) and \(\mathbf{a} \times \mathbf{b}=\mathbf{0}\), then \((m, n)\) is equal toAP EAMCET 2016 Easy
- A true statement among the following identities isAP EAMCET 2022 Medium
- For a perfect black body, the absorption coefficient isAP EAMCET 2020 Easy
- A cell of emf 1.2 V and internal resistance \(2 \Omega\) is connected in parallel to another cell of emf 1.5 V and internal resistance \(1 \Omega\). If the like poles of the cells are connected together, the emf of the combination of the two cells isAP EAMCET 2024 Easy