AP EAMCET · Maths · Vector Algebra
If \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are non-coplanar unit vectors such that \(\mathbf{a} \times(\mathbf{b} \times \mathbf{c})=\frac{\mathbf{b}+\mathbf{c}}{\sqrt{2}}\), then the angle between \(\mathbf{a}\) and \(\mathbf{b}\) is
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{2}\)
- D \(\frac{3 \pi}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{3 \pi}{4}\)
Step-by-step Solution
Detailed explanation
Since, \(\mathbf{a} \times(\mathbf{b} \times \mathbf{c})\) \[ =(\mathbf{a} \cdot \mathbf{c}) \cdot \mathbf{b}-(\mathbf{a} \cdot \mathbf{b}) \mathbf{c}=\frac{\mathbf{b}+\mathbf{c}}{\sqrt{2}} \quad (given) \] So,…
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 sum of the lengths of the subtangent and the subnormal drawn at \(\theta=\frac{\pi}{3}\) on the cycloid \(x=a(\theta-\sin \theta)\) : \(y=a(1-\cos \theta)\) isAP EAMCET 2021 Medium
- If the equation \(2 x^2+k x y-6 y^2+3 x+y+1=0\), \((k>0)\) represents a pair of straight lines, then their point of intersection isAP EAMCET 2021 Medium
- Let \((x, y) \in R \times R\) and \(\bar{a}=x \bar{i}+2 \bar{j}-\bar{k}, \bar{b}=6 \bar{i}-y \bar{j}+2 \bar{k}\) be two vectors. If \(|\overline{\mathrm{a}} \times \overline{\mathrm{b}}|^2+|\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}|^2=\mathrm{f}(\mathrm{x}) \mathrm{g}(\mathrm{y})\), then \(\mathrm{f}(\mathrm{x})+\mathrm{g}(\mathrm{y})-46=0\) representsAP EAMCET 2025 Medium
- For different real non-zero numbers \(x_1, x_2, x_3\) and \(x_4\), suppose the points \(\left(x_1, \frac{1}{x_1}\right),\left(x_2, \frac{1}{x_2}\right),\left(x_3, \frac{1}{x_3}\right)\) and \(\left(x_4, \frac{1}{x_4}\right)\) lie on the boundary of a circle of radius 4 . Then, the value of \(x_1 x_2 x_3 x_4\) isAP EAMCET 2022 Easy
- Let . Then maximum value of isAP EAMCET 2022 Medium
- For the function \(f(x)=(x-1)(x-2)\) defined on \(\left[0, \frac{1}{2}\right]\), the value of \(c\) satisfying Lagrange's mean value theorem isAP EAMCET 2017 Medium
More PYQs from AP EAMCET
- If \(\int \frac{x^2-x+2}{x^2+x+2} d x=x-\log (f(x))+\frac{2}{\sqrt{7}} \operatorname{Tan}^{-1}(g(x))+c\), then \(\mathrm{f}(-1)+\sqrt{7} \mathrm{~g}(-1)=\)AP EAMCET 2025 Medium
- Five different books are to be distributed among four students randomly. The probability that each child get atleast one book isAP EAMCET 2020 Medium
- If the equation
\(a x^2+2 h x y+b y^2+2 g x+2 f y+c=0\) represents two straight lines equidistant from the origin, then \(f^4-g^4=\)AP EAMCET 2020 Hard - If the tangent to the curve \(2 y^3=a x^2+x^3\) at the point \((a, a)\) cuts off intercepts \(\alpha\) and \(\beta\) on the coordinate axes, where \(\alpha^2+\beta^2=61\), then the value of \(|a|\) isAP EAMCET 2021 Medium
- \(50 \mathrm{~mL}\) of \(\mathrm{H}_2 \mathrm{O}\) is added to \(50 \mathrm{~mL}\) of \(1 \times 10^{-3} \mathrm{M}\) barium hydroxide solution. What is the \(\mathrm{pH}\) of the resulting solution?AP EAMCET 2008 Easy
- One mole of \(\mathrm{PCl}_5(\mathrm{~g})\) was heated in a \(1 \mathrm{~L}\) closed flask at \(500 \mathrm{~K}\). At equilibrium, 0.1 mole of \(\mathrm{Cl}_2(\mathrm{~g})\) was formed. What is its \(\mathrm{K}_{\mathrm{p}}\) (in atm)?
(Given \(\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\) )AP EAMCET 2023 Medium