Question:medium

If \( \mathbf{a} = 3\hat{i} + 4\hat{j} \) and \( \mathbf{b} = 2\hat{i} - \hat{j} \), find \( \mathbf{a} \cdot \mathbf{b} \) (the dot product).

Show Hint

Remember: The dot product of two vectors is calculated by multiplying their corresponding components and summing them.

Updated On: Nov 26, 2025

2
4
10
12

Top Questions on Vector Algebra

If \( \vec{a}, \vec{b}, \vec{c} \) are non-coplanar vectors and \( \lambda \) is a real number, then the vectors \( \vec{a} + 2\vec{b} + 3\vec{c} \), \( \lambda \vec{b} + 4\vec{c} \), and \( (2\lambda - 1)\vec{c} \) are non-coplanar for:
- WBJEE - 2025
- Mathematics
- Vector Algebra
View Solution
If \( \vec{\alpha} = 3\hat{i} - \hat{j} + \hat{k} \), \( |\vec{\beta}| = \sqrt{5} \) and \( \vec{\alpha} \cdot \vec{\beta} = 3 \), then the area of the parallelogram for which \( \vec{\alpha} \) and \( \vec{\beta} \) are adjacent sides is:
- WBJEE - 2025
- Mathematics
- Vector Algebra
View Solution
Let \( \vec{a}, \vec{b}, \vec{c} \) be unit vectors. Suppose \( \vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c} = 0 \) and the angle between \( \vec{b} \) and \( \vec{c} \) is \( \frac{\pi}{6} \). Then \( \vec{a} \) is:
- WBJEE - 2025
- Mathematics
- Vector Algebra
View Solution
If $ \mathbf{a} $ and $ \mathbf{b} $ are non-coplanar unit vectors such that $ \mathbf{a} \times (\mathbf{b} \times \mathbf{c}) = \frac{\mathbf{b}}{2} $ then the angle between $ \mathbf{a} $ and $ \mathbf{b} $ is:
- MHT CET - 2025
- Mathematics
- Vector Algebra
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in MHT CET exam

Which of the following has the lowest boiling point?

MHT CET - 2025
intermolecular forces

View Solution

Which of the following elements has the most electronegativity: Li, Na, K, or Rb?

MHT CET - 2025
Electronegativity

View Solution

Total pressure of the solution is 500, the partial pressure of component A is 400, and the partial pressure of component B is 575. What is the mole fraction of component B?

MHT CET - 2025
Mole concept and Molar Masses

View Solution

What is the number of unpaired electrons in Lutetium (Lu) in the +3 oxidation state?

MHT CET - 2025
Oxidation Number And Oxidation States

View Solution