TS EAMCET · Maths · Vector Algebra
The acute angle between \(\mathbf{r}=(-\hat{\mathbf{i}}+3 \hat{\mathbf{k}})+\lambda(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}})\) and \(\mathbf{r} \cdot(10 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-11 \hat{\mathbf{k}})=3\), is
- A \(\sin ^{-1}\left(\frac{8}{21}\right)\)
- B \(\cos ^{-1}\left(\frac{8}{21}\right)\)
- C \(\sin ^{-1}\left(\frac{5}{21}\right)\)
- D \(\cos ^{-1}\left(\frac{5}{21}\right)\)
Answer & Solution
Correct Answer
(A) \(\sin ^{-1}\left(\frac{8}{21}\right)\)
Step-by-step Solution
Detailed explanation
Given, \(\begin{aligned} & r=(-\hat{\mathbf{i}}+3 \hat{\mathbf{k}})+\lambda(2 \hat{\mathbf{i}}+3 \hat{\mathrm{j}}+6 \hat{\mathbf{k}}) \\ & \text{and } \mathbf{r} \cdot(10 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}-11 \hat{\mathbf{k}})=3 \end{aligned}\) If angle between line and plane…
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 normal at a point to the curve always passes through the fixed pointTS EAMCET 2018 Medium
- If \(x^2+y^2=t+\frac{2}{t}\) and \(x^4+y^4=t^2+\frac{4}{t^2}\), then \(x^3 y \frac{d y}{d x}\) equalsTS EAMCET 2015 Easy
- If the tangents \(x+y+k=0\) and \(x+a y+b=0\) drawn to the circle \(S \equiv x^2+y^2+2 x-2 y+1=0\) are perpendicular to each other and \(k, b\) are both greater than 1 , then \(b-k=\)TS EAMCET 2024 Easy
- be an increasing function such that for all . If thenTS EAMCET 2020 Medium
- If \(\theta\) is the acute angle between the curves \(x^2+y^2=2020 \sqrt{2}\) and \(x^2-y^2=2020\), then \(\frac{\sin \theta+\cos \theta}{\tan \theta}\) is equal toTS EAMCET 2021 Hard
- Consider the parabola \(25\left[(x-2)^2+(y+5)^2\right]=(3 x+4 y-1)^2\) match the characteristic of this parabola given in List-I with its corresponding item in List-II.
The correct answer isTS EAMCET 2024 Easy
More PYQs from TS EAMCET
- For all \(x \in R\), the minimum value \(\frac{1}{3}\) and the maximum value 3 of \(\frac{x^2+x+1}{x^2-x+1}\) exist at \(l\) and \(m\) respectively, then \(l+m\) is equal toTS EAMCET 2021 Easy
- If the line \(x+y=2\) cuts the circle \(x^2+y^2+2 x-4 y+4=0\) at two points A and B then the radius of the circle passing through \(\mathrm{A}, \mathrm{B}\) and orthogonal to \(x^2+y^2-2 x-4 y-4=0\) isTS EAMCET 2025 Hard
- If the algebraic sum of the perpendicular distances from the points \((2,0),(0,2)\) and \((1,1)\) to a variable line is zero, then the variable line always passes through a fixed point. The coordinates of that point areTS EAMCET 2022 Easy
- Standard enthalpy (heat) of formation of liquid water at \(25^{\circ} \mathrm{C}\) is around \[ \mathrm{H}_2(g)+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \]TS EAMCET 2017 Hard
- A bomb moving with velocity \((40 \hat{\mathbf{i}}+50 \hat{\mathbf{j}}-25 \hat{\mathbf{k}}) \mathrm{m} / \mathrm{s}\) explodes into two pieces of mass ratio \(1: 4\). After explosion the smaller piece moves away with velocity \((200 \hat{\mathbf{i}}+70 \hat{\mathbf{j}}+15 \hat{\mathbf{k}}) \mathrm{m} / \mathrm{s}\). The velocity of larger piece after explosion isTS EAMCET 2010 Medium
- A circular hoop of radius and mass rotating with an angular velocity is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. Let be the velocity of the centre of the hoop when it ceases to slip. The ratio will beTS EAMCET 2021 Easy