enEnglishguગુજરાતી
JEE Mains · Maths · STD 12 - 10. vector algebra
If \(\hat a,\,\hat b\) and \(\hat c\) are unit vectors satisfying \(\hat a\, - \,\sqrt 3 \hat b + \hat c\, = \,\vec 0,\) then the angle between the vectors \(\hat a\) and \(\hat c\) is
- A \(\frac {\pi }{4}\)
- B \(\frac {\pi }{3}\)
- C \(\frac {\pi }{6}\)
- D \(\frac {\pi }{2}\)
Answer & Solution
Correct Answer
(B) \(\frac {\pi }{3}\)
Step-by-step Solution
Detailed explanation
Let angle between \(\hat{a}\) and \(\hat{c}\) be \(\theta\) Now, \(\hat{a}-\sqrt{3} \hat{b}+\hat{c}=\overrightarrow{0}\) \(\Rightarrow(\hat{a}+\hat{c})=\sqrt{3} \hat{b}\) \(\Rightarrow(\hat{a}+\hat{c}) \cdot(\hat{a}+\hat{c})=3(\hat{b} \cdot \hat{b})\)…
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
- Let \(R\) be a relation on \(Z \times Z\) defined by\( (a, b)\)\(R(c, d)\) if and only if \(ad - bc\) is divisible by \(5\) . Then \(\mathrm{R}\) isJEE Mains 2024 Medium
- If the Rolle's theorem holds for the function \(f(x) = 2x^3 + ax^2 + bx\) in the interval \([-1, 1 ]\) for the point \(c = \frac{1}{2}\) , then the value of \(2a + b\) isJEE Mains 2015 Hard
- Let \(\alpha\) and \(\beta\) be the roots of \(x^2+\sqrt{3 x}-16=0\), and \(\gamma\) and \(\delta\) be the roots of \(x^2+3 x-1=0\). If \(P_n=\alpha^n+\beta^n\) and \(Q_n=\gamma^n+\delta^n\), then \(\frac{\mathrm{P}_{25}+\sqrt{3 \mathrm{P}_{24}}}{2 \mathrm{P}_{23}}+\frac{\mathrm{Q}_{25}-\mathrm{Q}_{23}}{\mathrm{Q}_{24}}\) is equal toJEE Mains 2025 Medium
- If the mirror image of the point \((1,3,5)\) with respect to the plane \(4 x -5 y +2 z =8\) is \((\alpha, \beta, \gamma)\) then \(5(\alpha+\beta+\gamma)\) equals ...... ..JEE Mains 2021 Hard
- The set of values of \(a\) for which \(\lim _{x \rightarrow a}([x-5]-[2 x+2])=0\), where, \([\zeta]\) denotes the greatest integer less than or equal to \(\zeta\) is equal toJEE Mains 2023 Medium
- If \(\alpha \) and \(\beta \) are the roots of the quadratic equation, \(x^2 + x\, sin\,\theta -2sin\,\theta = 0\), \(\theta \in \left( {0,\frac{\pi }{2}} \right)\) then \(\frac{{{\alpha ^{12}} + {\beta ^{12}}}}{{\left( {{\alpha ^{ - 12}} + {\beta ^{ - 12}}} \right){{\left( {\alpha - \beta } \right)}^{24}}}}\) is equal toJEE Mains 2019 Hard
More PYQs from JEE Mains
- The sum \(1+3+11+25+45+71+.\). upto 20 terms, is equal toJEE Mains 2025 Medium
- The sum \(1^2-2.3^2+3.5^2-4.7^2+5.9^2-\ldots +15.29^2\) is \(.......\).JEE Mains 2023 Hard
- Let \(A\) be a \(3 \times 3\) matrix such that \(A^T \begin{bmatrix}1\\0\\1\end{bmatrix} = \begin{bmatrix}5\\2\\2\end{bmatrix}\), \(A^T \begin{bmatrix}0\\0\\1\end{bmatrix} = \begin{bmatrix}3\\1\\1\end{bmatrix}\), \(A \begin{bmatrix}1\\0\\1\end{bmatrix} = \begin{bmatrix}3\\4\\4\end{bmatrix}\) and \(A \begin{bmatrix}0\\0\\1\end{bmatrix} = \begin{bmatrix}1\\3\\1\end{bmatrix}\). If \(\det(A) = 1\), then \(\det(\operatorname{adj}(A^2 + A))\) is equal to:JEE Mains 2026 Hard
- Let \(\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \quad \vec{b}=2 \hat{i}+3 \hat{j}-5 \hat{k} \quad\) and \(\overrightarrow{\mathrm{c}}=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}\) be three vectors. Let \(\overrightarrow{\mathrm{r}}\) be a unit vector along \(\vec{b}+\vec{c}\). If \(\vec{r} . \vec{a}=3\), then \(3 \lambda\) is equal to :JEE Mains 2024 Medium
- Using the principal values of the inverse trigonometric functions, the sum of the maximum and the minimum values of \(16\left(\left(\sec ^{-1} x\right)^2+\left(\operatorname{cosec}^{-1} x\right)^2\right)\) is :JEE Mains 2025 Medium
- If \(x\, = a\), \(y\, = b\), \(z\, = c\) is a solution of the system of linear equations \(x+8y+ 7z\,= 0\) ; \(9x+ 2y+ 3z\, = 0\) ; \(x+y+z\, = 0\) such that the point \((a, b, c)\) lies on the plane \(x + 2y + z\, = 6\), then \(2a + b + c\) equalsJEE Mains 2017 Hard