TS EAMCET · Maths · Vector Algebra
If the angle between the planes \(\bar{r} \cdot(11 \hat{i}-2 \hat{j}+\alpha \hat{k})=7\) and \(\bar{r} \cdot(2 \hat{i}+4 \hat{j}-2 \hat{k})=5\) is \(\frac{\pi}{2}\), then \(\alpha=\)
- A 2
- B 3
- C 5
- D 7
Answer & Solution
Correct Answer
(D) 7
Step-by-step Solution
Detailed explanation
Given planes are \(\bar{r} \cdot(11 \hat{i}-2 \hat{j}-\alpha \hat{k})=7\) and \(\overline{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}-2 \hat{\mathrm{k}})=5\) \(\Rightarrow \mathrm{n}_1 \cdot \mathrm{n}_2=0 \Rightarrow 22-8-2 \alpha=0\) or \(\alpha=7\)
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
- For if term is the first negative term in the expansion of and in the expansion of from term onwards all the terms are positive, then the number of terms in the expansion of isTS EAMCET 2021 Easy
- Let \(\mathrm{A}(\alpha, 4,7)\) and \(\mathrm{B}(3, \beta, 8)\) be two points in space. If YZ plane and ZX plane respectively divide the line segment joining the points A and B in the ratio \(2: 3\) and 4:5, then the point C which divides \(\overline{\mathrm{AB}}\) in the ratio \(\alpha: \beta\) externally isTS EAMCET 2025 Medium
- For the ellipse \(4 x^2+y^2-8 x+2 y+1=0\), the focus and the equation of the directrix are respectivelyTS EAMCET 2018 Medium
- If the coefficient of \((2 r+1)\) th term and \((r+2)\) th term in the expansion of \((1+x)^{43}\) are equal, then \(r\) is equal to :TS EAMCET 2003 Easy
- A fair coin is tossed \(K\) times so that the probability of getting four heads is equal to that of getting six heads. If the probability is maximum for getting \(r\) heads then \(r=\)TS EAMCET 2020 Easy
- Area of the region (in sq units) bounded by the curves \(y=\sqrt{x}, x=\sqrt{y}\) and the lines \(x=1\), \(x=4\), isTS EAMCET 2019 Medium
More PYQs from TS EAMCET
- In a pair of adjacent coils if the current in one coil changes from \(10 \mathrm{~A}\) to \(2 \mathrm{~A}\) in a time \(0.2 \mathrm{~s}\), an emf of \(120 \mathrm{~V}\) is induced in another coil. The mutual inductance of the pair of the coils isTS EAMCET 2023 Medium
- Three rods \(A B, B C\) and \(B D\) made of the same material and having the same cross-section have been joined as shown in the figure.
The ends \(A, C\) and \(D\) are held at temperatures of \(20^{\circ} \mathrm{C}, 80^{\circ} \mathrm{C}\) and \(80^{\circ} \mathrm{C}\) respectively. If each rod is of same length, then the temperature at the junction \(B\) of the three rods isTS EAMCET 2010 Easy - Consider a rod of length, with a cross-sectional area of The rod supports a , platform that hangs attached to the rod's lower end. What is the elongation of the rod under the stress ignoring the weight of the rod? Consider Young's modulus to be andTS EAMCET 2021 Medium
- Match the following.
The correct answer is \(\begin{array}{llll} \text { A } & \text { B } & \text { C } & \text { D } \end{array}\)TS EAMCET 2022 Hard - Two vessels separately contain two ideal gases and at the same temperature. The pressure of gas is three times the pressure of gas . Under these conditions, the density of gas is found to be two times the density of . The ratio of molecular weights of gas and i.e. isTS EAMCET 2020 Hard
- The general solution of \(\frac{d y}{d x}=\frac{x^3\left(y^4+1\right)}{[}\) is \[ \left[2 y^{-\frac{2}{3}}+3\left(\frac{x}{\sqrt[3]{y}}\right)^2\right]^{\frac{3}{2}} \]TS EAMCET 2021 Hard