AP EAMCET · Maths · Vector Algebra
Find ' \(\lambda\) ' if \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are three non-coplanar vectors such that
\(\left[\begin{array}{ccc}
4 a+3 b-c & 4 a+3 b+2 c \quad a-4 b-c
\end{array}\right]\)
\(=\left(\lambda^2+\lambda+1\right)\left[\begin{array}{lll}a & b & c\end{array}\right]\)
- A \(-7,8\)
- B \(-7,-6\)
- C \(7,-8\)
- D \(-7,-8\)
Answer & Solution
Correct Answer
(C) \(7,-8\)
Step-by-step Solution
Detailed explanation
\begin{array}{rlrl} \left|\begin{array}{ccc} 4 & 3 & -1 \\ 4 & 3 & 2 \\ 1 & -4 & -1 \end{array}\right|[\bar{a} \bar{b} \bar{c}] & =\left(\lambda^2+\lambda+1\right)[\bar{a} \bar{b} \bar{c}] \\ 4(5)-3(-6)-1(-19) & =\lambda^2+\lambda+1 \\ 57 & =\lambda^2+\lambda+1 \\ \Rightarrow &…
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 derivative of \(y=\sin ^{-1}\left(\frac{\sqrt{1+x}-\sqrt{1-x}}{2}\right)\) isAP EAMCET 2020 Medium
- If \(x^3+y^3=3 a x y\), then at \(\left(\frac{3 a}{2}, \frac{3 a}{2}\right)\) the value of \(3 a y^{\prime \prime}+40\) isAP EAMCET 2023 Easy
- If \(k \in N\) then \(\lim _{n \rightarrow \infty}\left[\frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+\ldots+\frac{1}{k n}\right]=\)AP EAMCET 2025 Medium
- The equation of a curve passing through the point \((0,1)\), given that the slope of the tangent to the curve at any point \((x, y)\) is equal to the sum of the \(x\)-coordinate and the product of \(x\) and \(y\) coordinates at that point, isAP EAMCET 2021 Medium
- If \(f(x+a y)+g(x-a y)=0\), then \(a \frac{d y}{d x}=\)AP EAMCET 2023 Medium
- If \(\frac{x^2}{a}+\frac{2 x y}{h}+\frac{y^2}{b}=0\) represents a pair of straight lines such that the slope of one of the lines is twice the other, then \(\frac{a b}{h^2}=\)AP EAMCET 2017 Medium
More PYQs from AP EAMCET
- \(\int \sqrt{x+\sqrt{x^2+2}} d x=\)AP EAMCET 2022 Easy
- A motor of power \(P_0\) is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe \(n\) times, the power of the motor is increased to \(P_1\). The ratio of \(P_1\) to \(P_0\) isAP EAMCET 2009 Easy
- The descending order of magnitude of the eccentricities of the following hyperbolas is
A. A hyperbola whose distance between foci is three times the distance between its directrices.
B. Hyperbola in which the transverse axis is twice the conjugate axis.
C. Hyperbola with asymptotes
\(x+y+1=0, x-y+3=0\)AP EAMCET 2024 Easy - Which reaction among the following will yield 2,2-dibromopropane?AP EAMCET 2020 Medium
- A light ray incidents on an equilateral prism made of material of refractive index \(\sqrt{3}\). Inside the prism, if the light ray moves parallel to the base of the prism, then the angle of incidence of the light ray isAP EAMCET 2025 Medium
- If the coefficients of \(r\) th and \((r+1)\) th terms in the expansion of \((3+7 x)^{29}\) are equal, then \(r\) is equal toAP EAMCET 2011 Easy