Practice Dot Product (Scalar Product) - 5.5.4 | 5. Vectors | ICSE 12 Mathematics
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 (Scalar Product)

5.5.4 - Dot Product (Scalar 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

What is the dot product of \( \vec{A} = (1, 2) \) and \( \vec{B} = (3, 4) \)?

💡 Hint: Use the formula \\( A_xB_x + A_yB_y \\).

Question 2 Easy

Is the result of a dot product a vector or a scalar?

💡 Hint: Think about what kind of quantity a dot product yields.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the dot product yield?

A vector
A matrix
A scalar

💡 Hint: Remember, it gives a number, not a direction.

Question 2

If \( \vec{A} \cdot \vec{A} = 0 \), what can be said about \( \vec{A} \)?

True
False

💡 Hint: Think about vectors and their magnitudes.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given two vectors, \( \vec{A} = (2, 3, 4) \) and \( \vec{B} = (-1, 0, 5) \), find \( \vec{A} \cdot \vec{B} \) and interpret the result in terms of direction.

💡 Hint: Apply the dot product formula and sum the results carefully.

Challenge 2 Hard

If \( |\vec{A}| = 5 \) and \( |\vec{B}| = 12 \) with an angle of \( 60^\circ \) between them, calculate \( \vec{A} \cdot \vec{B} \)

💡 Hint: Use the cosine value and multiply it with the magnitudes.

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.