Let \(→{b}=^i+^j+λ k\) , λ ∈ R. If vector a is a vector such that → a×→ b= 13^i −^j−4^k and→ a.→ b+ 21 =0, then (→ b − → a) . ( → k − ^ j ) + ( → b + → a ) . ( ^ i − ^ k ) is equal to
Correct Answer: 14
Solution and Explanation
The correct answer is: 14.
Top Questions on Vectors
যদি \( \vec{a} = 4\hat{i} - \hat{j} + \hat{k} \) এবং \( \vec{b} = 2\hat{i} - 2\hat{j} + \hat{k} \) হয়, তবে \( \vec{a} + \vec{b} \) ভেক্টরের সমান্তরাল একটি একক ভেক্টর নির্ণয় কর।
যদি ভেক্টর \( \vec{\alpha} = a\hat{i} + a\hat{j} + c\hat{k}, \quad \vec{\beta} = \hat{i} + \hat{k}, \quad \vec{\gamma} = c\hat{i} + c\hat{j} + b\hat{k} \) একই সমতলে অবস্থিত (coplanar) হয়, তবে প্রমাণ কর যে \( c^2 = ab \)।
- If the sum of two vectors is a unit vector, then the magnitude of their difference is:
- Let \( \vec{a} \) be a position vector whose tip is the point (2, -3). If \( \overrightarrow{AB} = \vec{a} \), where coordinates of A are (–4, 5), then the coordinates of B are:
The respective values of \( |\vec{a}| \) and} \( |\vec{b}| \), if given \[ (\vec{a} - \vec{b}) \cdot (\vec{a} + \vec{b}) = 512 \quad \text{and} \quad |\vec{a}| = 3 |\vec{b}|, \] are:
Questions Asked in JEE Main exam
- Two tuning forks \(A\) and \(B\) are sounded together giving rise to 8 beats in 2 s. When fork \(A\) is loaded with wax, the beat frequency is reduced to 4 beats in 2 s. If the original frequency of tuning fork \(B\) is \(380\ \text{Hz}\), find the original frequency of tuning fork \(A\). Given: \[ f_B = 380\ \text{Hz} \]
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- General Physics
Let the lines $L_1 : \vec r = \hat i + 2\hat j + 3\hat k + \lambda(2\hat i + 3\hat j + 4\hat k)$, $\lambda \in \mathbb{R}$ and $L_2 : \vec r = (4\hat i + \hat j) + \mu(5\hat i + + 2\hat j + \hat k)$, $\mu \in \mathbb{R}$ intersect at the point $R$. Let $P$ and $Q$ be the points lying on lines $L_1$ and $L_2$, respectively, such that $|PR|=\sqrt{29}$ and $|PQ|=\sqrt{\frac{47}{3}}$. If the point $P$ lies in the first octant, then $27(QR)^2$ is equal to}
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- Let \(y=y(x)\) be the solution of the differential equation \[ x\frac{dy}{dx}=y-x^2\cot x,\quad x\in(0,\pi) \] If \(y\!\left(\frac{\pi}{2}\right)=\frac{\pi^2}{2}\), then \[ 6y\!\left(\frac{\pi}{6}\right)-8y\!\left(\frac{\pi}{4}\right) \] is equal to:
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- The sum of the coefficients of \(x^{499}\) and \(x^{500}\) in \[ (1+x)^{1000}+x(1+x)^{999}+x^2(1+x)^{998}+\cdots+x^{1000} \] is:
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Concepts Used:
Vector Basics
What is a Vector Quantity?
Vector Quantity is a physical quantity that is specified not only by its magnitude but also by its direction. A vector quantity whose magnitude is equal to one and has direction is called a unit vector.
Examples of vector quantity are-
- Displacement
- Linear momentum
- Momentum
- Acceleration
- Force
- Electric field
- Angular velocity
- Polarization