Question:
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
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
Updated On: Mar 2, 2024
Hide Solution
Verified By Collegedunia
Correct Answer: 14
Solution and Explanation
The correct answer is: 14.
Was this answer helpful?
0
2
Top Questions on Vectors
- Let $ \vec{a} = \hat{i} + 2 \hat{j} + \hat{k} $ and $ \vec{b} = 2 \hat{i} + \hat{j} - \hat{k} $. Let $ \hat{c} $ be a unit vector in the plane of the vectors $ \vec{a} $ and $ \vec{b} $ and perpendicular to $ \vec{a} $. Then such a vector $ \hat{c} $ is:
- Let A be the point of intersection of the lines $$ L_1 : \frac{x - 7}{1} = \frac{y - 5}{0} = \frac{z - 3}{-1} \quad \text{and} \quad L_2 : \frac{x - 1}{3} = \frac{y + 3}{4} = \frac{z + 7}{5}$$ Let B and C be the points on the lines $ L_1 $ and $ L_2 $, respectively, such that $ AB - AC = \sqrt{15} $. Then the square of the area of the triangle ABC is:
- Let \( \mathbf{a} \), \( \mathbf{b} \), and \( \mathbf{c} \) be vectors of magnitude 2, 3, and 4 respectively. If: - \( \mathbf{a} \) is perpendicular to \( (\mathbf{b} + \mathbf{c}) \), - \( \mathbf{b} \) is perpendicular to \( (\mathbf{c} + \mathbf{a}) \), - \( \mathbf{c} \) is perpendicular to \( (\mathbf{a} + \mathbf{b}) \), then the magnitude of \( \mathbf{a} + \mathbf{b} + \mathbf{c} \) is equal to:
- If the sum of two vectors is a unit vector, then the magnitude of their difference is:
- Number of functions \( f: \{1, 2, \dots, 100\} \to \{0, 1\} \), that assign 1 to exactly one of the positive integers less than or equal to 98, is equal to:
View More Questions
Questions Asked in JEE Main exam
- A force \( \mathbf{F} = 2\hat{i} + b\hat{j} + \hat{k} \) is applied on a particle and it undergoes a displacement \( \mathbf{r} = \hat{i} - 2\hat{j} - \hat{k} \). What will be the value of \( b \), if the work done on the particle is zero?
- JEE Main - 2025
- Work and Energy
- A body of mass \(4\) kg is placed at a point \(P\) having coordinates \( (3,4) \) m. Under the action of force \( \mathbf{F} = (2\hat{i} + 3\hat{j}) \) N, it moves to a new point \(Q\) having coordinates \( (6,10) \) m in \(4\) sec. The average power and instantaneous power at the end of \(4\) sec are in the ratio:
- If the equation of the parabola with vertex $\left(\frac{3}{2},\, 3\right)$ and the directrix $x + 2y = 0$ is
$$ ax^2 + by^2 - cxy - 30x - 60y + 225 = 0, $$ then $\alpha + \beta + \gamma$ is equal to:- JEE Main - 2025
- Calculus
- An AC current is represented as: $ i = 5\sqrt{2} + 10 \cos\left(650\pi t + \frac{\pi}{6}\right) \text{ Amp} $ The RMS value of the current is:
- JEE Main - 2025
- AC Circuits
- HA $ (aq) \rightleftharpoons H^+ (aq) + A^- (aq) $ The freezing point depression of a 0.1 m aqueous solution of a monobasic weak acid HA is 0.20 °C. The dissociation constant for the acid is Given: $ K_f(H_2O) = 1.8 \, \text{K kg mol}^{-1} $, molality ≡ molarity
- JEE Main - 2025
- Colligative Properties
View More Questions
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