Practice Dot Product - 2.1 | 1. A vector and its representation | Solid Mechanics
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

Dot Product

2.1 - Dot Product

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.

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Calculate the dot product for vectors a = (1, 2) and b = (3, 4).

💡 Hint: Use the formula a · b = a1 * b1 + a2 * b2.

Question 2 Easy

What is the dot product of a vector with itself, for example, c = (5, 5)?

💡 Hint: Remember, the dot product of a vector with itself yields the square of its magnitude.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the result of the dot product between two perpendicular vectors?

1
0
-1

💡 Hint: Remember the geometric interpretation.

Question 2

True or False: The dot product yields a vector result.

True
False

💡 Hint: Think about the nature of the output.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given three vectors: a = (3, 1, 2), b = (1, 4, 0), and c = (2, -1, 3), find the dot product of a and b, and then determine the angle between c and the resultant vector of a and b.

💡 Hint: Don't forget to calculate the magnitudes for the final angle determination.

Challenge 2 Hard

Two vectors have a dot product of -12, Suggest possible values for their magnitudes and the angle between them.

💡 Hint: Think about how multiplying positive and negative components give a negative value?

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.