5.5 - Operations on Vectors
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
Add the vectors \(\vec{A} = 1\hat{i} + 2\hat{j}\) and \(\vec{B} = 3\hat{i} + 4\hat{j}\).
💡 Hint: Combine corresponding components.
What happens to a vector when multiplied by a scalar of 0?
💡 Hint: Consider what multiplying by zero does.
1 more question available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the result of the dot product of two perpendicular vectors?
💡 Hint: Think about the relationship of angles between vectors.
True or false: The cross product of two vectors results in a scalar.
💡 Hint: Consider what you learned about vector products.
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
Given vectors \(\vec{A} = 3\hat{i} + 4\hat{j}\, and \(\vec{B} = 5\hat{i} + 6\hat{j} + 1\hat{k}\), calculate both their dot and cross products.
💡 Hint: Break it down into component calculations for both products.
A particle is moving along vector \(\vec{A} = 50\hat{i} + 100\hat{j}\) and is affected by a force represented by \(\vec{B} = -30\hat{i} + 20\hat{j}\). Calculate the resultant vector and discuss what this vector implies about the particle's new position.
💡 Hint: Use component addition to find the resultant direction.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.