JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}, \vec{b}\) and \(\vec{c}\) be three vectors such that \(\vec{a}=\vec{b} \times(\vec{b} \times \vec{c}) .\) If magnitudes of the vectors \(\vec{a}, \vec{b}\) and \(\vec{c}\) are \(\sqrt{2}, 1\) and 2 respectively and the angle between \(\vec{b}\) and \(\vec{c}\) is \(\theta\left(0<\theta<\frac{\pi}{2}\right)\), then the value of \(1+\tan \theta\) is equal to:
- A \(\frac{\sqrt{3}+1}{\sqrt{3}}\)
- B \(2\)
- C \(\sqrt{3}+1\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(\vec{a}=(\vec{b} \cdot \vec{c}) \vec{b}-(\vec{b} \cdot \vec{b}) \vec{c}\) \(=1.2 \cos \theta \vec{b}-\vec{c} b\) \(\Rightarrow \quad \vec{a}=2 \cos \theta \vec{b}-\vec{c}\) \(|\vec{a}|^{2}=(2 \cos \theta)^{2}+2^{2}-2 \cdot 2 \cos \theta \vec{b} \cdot \vec{c}\)…
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
- Suppose that a function \(f: R \rightarrow R\) satisfies \(f(x+y)=f(x) f(y)\) for all \(x, y \in R\) and \(f(1)=3 .\) If \(\sum \limits_{i=1}^{n} f(i)=363,\) then \(n\) is equal toJEE Mains 2020 Medium
- If \(\frac{d y}{d x}=\frac{x y}{x^{2}+y^{2}} ; y(1)=1 ;\) then a value of \(x\) satisfying \(\mathrm{y}(\mathrm{x})=\mathrm{e}\) isJEE Mains 2020 Hard
- Let \([\cdot]\) denote the greatest integer function. If the domain of the function \(f(x) = \cos^{-1}\left(\dfrac{4x+2[x]}{3}\right)\) is \([\alpha, \beta]\), then \(12(\alpha + \beta)\) is equal to:JEE Mains 2026 Medium
- Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is \(840\), then the total numbers of persons, who participated in the tournament, is \(........\).JEE Mains 2023 Medium
- If \(P=\left[\begin{array}{ll}1 & 0 \\ 1 / 2 & 1\end{array}\right]\), then \(P^{50}\) is:JEE Mains 2021 Medium
- Let the complex numbers \(\alpha\) and \(\frac{1}{\bar{\alpha}}\) lie on the circles \(\left|z-z_0\right|^2=4\) and \(z-\left.z_0\right|^2=16\) respectively, where \(z_0=1+i\). Then, the value of \(100|\alpha|^2\) is.JEE Mains 2024 Hard
More PYQs from JEE Mains
- Let \(A\) be the area bounded by the curve \(y=x|x-3|\), the \(x\)-axis and the ordinates \(x=-1\) and \(x=2\). Then \(12\,A\) is equal to \(...........\).JEE Mains 2023 Hard
- A rod of length eight units moves such that its ends \(A\) and \(B\) always lie on the lines \(x-y+2=0\) and \(y+2=0\), respectively. If the locus of the point \(P\), that divides the rod \(A B\) internally in the ratio \(2: 1\) is \(9\left(x^2+\alpha y^2+\beta x y+\gamma x+28 y\right)-76=0\), then \(\alpha-\beta-\gamma\) is equal to :JEE Mains 2025 Hard
- Let \(A\) and \(E\) be any two events with positive probabilities:
Statement \(- 1\): \(P\left( {E/A} \right) \geq P\left( {A/E} \right)P\left( E \right)\)
Statement \(-2\) : \(P\left( {A/E} \right) \geq P\left( {A \cap E} \right)\)JEE Mains 2014 Hard - In a parallelogram \(ABCD\), \(\left| {\overline {AB} } \right| = a\,,\,\left| {\overline {AD} } \right| = b\) and \(\left| {\overline {AC} } \right| = c\) then \(\overline {DA} \). \(\overline {AB} \) has the valueJEE Mains 2015 Hard
- If \(\left({ }^{30} C _1\right)^2+2\left({ }^{30} C _2\right)^2+3\left({ }^{30} C _3\right)^2+\ldots \ldots+30\left({ }^{30} C _{30}\right)^2=\) \(\frac{\alpha 60 !}{(30 !)^2}\), then \(\alpha\) is equal toJEE Mains 2023 Hard
- Let the length of the focal chord \(P Q\) of the parabola \(y^2=12 x\) be \(15\) units. If the distance of \(P Q\) from the origin is \(\mathrm{p}\), then \(10 \mathrm{p}^2\) is equal to ...........JEE Mains 2024 Hard