AP EAMCET · Maths · Vector Algebra
\(\begin{aligned} & \text { If } \mathbf{a}=\mathbf{i}+\mathbf{j}+\mathbf{k}, \mathbf{b}=2 \mathbf{i}-\mathbf{j}+3 \mathbf{k} \text { and } \mathbf{c}=\mathbf{i}-\mathbf{j} \\ & \text { and if } 6 \mathbf{i}+2 \mathbf{j}+3 \mathbf{k}=\lambda_1(\mathbf{a} \times \mathbf{b}) \\ & +\lambda_2(\mathbf{b} \times \mathbf{c})+\lambda_3(\mathbf{c} \times \mathbf{a}) \text {, then }\left(\lambda_1, \lambda_2, \lambda_3\right)=\end{aligned}\)
- A \(\left(\frac{11}{5}, \frac{4}{5}, \frac{19}{5}\right)\)
- B \(\left(\frac{4}{5}, \frac{11}{5}, \frac{19}{5}\right)\)
- C \(\left(\frac{4}{5}, \frac{19}{5}, \frac{11}{5}\right)\)
- D \(\left(\frac{19}{5}, \frac{11}{5}, \frac{4}{5}\right)\)
Answer & Solution
Correct Answer
(B) \(\left(\frac{4}{5}, \frac{11}{5}, \frac{19}{5}\right)\)
Step-by-step Solution
Detailed explanation
Let \(\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{k}, \mathbf{b}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) and \(\mathbf{c}=\hat{\mathbf{i}}-\hat{\mathbf{j}}\)…
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
- In a \(\triangle \mathrm{ABC}\) if \(a=13, b=14, c=15\) then \(r_1=\)AP EAMCET 2024 Easy
- Let \(\vec{a}, \vec{b}, \vec{c}\) be three vectors such that \(\vec{a}\) is perpendicular to \(\overrightarrow{\mathrm{b}}\) and \(\overrightarrow{\mathrm{b}}\) is perpendicular to \(\overrightarrow{\mathrm{c}}\). If \(|\overrightarrow{\mathrm{a}}|=2,|\overrightarrow{\mathrm{b}}|=3,|\overrightarrow{\mathrm{c}}|=5\) and \(|\vec{a}+\vec{b}+\vec{c}|=4 \sqrt{3}\), then the angle between \(\vec{a}\) and \(\vec{c}\) isAP EAMCET 2023 Easy
- If \(\frac{1}{(3 x+1)(x-2)}=\frac{A}{3 x+1}+\frac{B}{x-2}\) and \(\frac{x+1}{(3 x+1)(x-2)}=\frac{C}{3 x+1}+\frac{D}{x-2}\), thenAP EAMCET 2024 Easy
- Two cards are drawn at random from a pack of 52 playing cards. If both the cards drawn are found to be black in colour, then the probability that atleast one of them is a face card isAP EAMCET 2025 Medium
- If \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3+a x^2+b x+c=0\), then \((\alpha+\beta-2 \gamma)(\beta+\gamma-2 \alpha)(\gamma+\alpha-2 \beta)=\)AP EAMCET 2025 Medium
- If is a pentagon, then the resultant of forces and isAP EAMCET 2020 Medium
More PYQs from AP EAMCET
- When the temperature difference between the source and sink increases, the efficiency of the heat engineAP EAMCET 2020 Easy
- If \({ }^{n-3} C_r+B^{n-3} C_{r-1}+B^{\prime n-3} C_{r-2}+{ }^{n-3} C_{r-3}\) \(={ }^n C_r\) holds. for all \(n \geq r \geq 3\), then \(\left(B \cdot B^{\prime}\right)=\).AP EAMCET 2022 Hard
- Identify the method of preparation of a colloidal sol from the followingAP EAMCET 2024 Easy
- Polymers that can be softened on heating and hardened on cooling are calledAP EAMCET 2024 Easy
- The maximum and minimum values of the function \(f:[R \rightarrow[R\) defined by \(f(x)=5 \cos x+3 \cos \left(x+\frac{\pi}{3}\right)+8\) for all \(x \in[R\), are respectively.AP EAMCET 2018 Medium
- If \(\frac{3 x+2}{(x+1)\left(2 x^2+3\right)}=\frac{A}{x+1}+\frac{B x+C}{2 x^2+3}\), then \(A+C-B\) is equal to :AP EAMCET 2006 Easy