We’re Open - Call Now!

Call Now to Set Up Tutoring

(888) 736-0920

Become a math whiz with AI Tutoring, Practice Questions & more.

We’re Open - Call Now!

Call Now to Set Up Tutoring

(888) 736-0920

The cross product is an essential concept in vector mathematics, especially in physics and engineering. It involves the multiplication of two vectors to produce a new vector that is perpendicular to both input vectors. The cross product is typically used to calculate the area of a parallelogram, the torque applied to an object, and the orientation of magnetic and electric fields.

To calculate the cross product of two vectors A and B in three-dimensional space, we use the following formula:

A x B = (A_{y} * B_{z} - A_{z} * B_{y}) i - (A_{x} * B_{z} - A_{z} * B_{x}) j + (A_{x} * B_{y} - A_{y} * B_{x}) k

where A

The cross product is anticommutative, meaning:

A x B = - (B x A)

The cross product is distributive:

A x (B + C) = A x B + A x C

The scalar multiplication property:

(kA) x B = A x (kB) = k(A x B)

where k is a scalar.
Given two vectors

A = (2, 3, 4)

and B = (5, 6, 7)

, we can calculate their cross product as follows:A x B = (3 * 7 - 4 * 6) i - (2 * 7 - 4 * 5) j + (2 * 6 - 3 * 5) k

= (-3) i - (-6) j + (-3) k

=

= (-3) i - (-6) j + (-3) k

=

-3, 6, -3>

In this example, the cross product of vectors A and B is the vector

-3, 6, -3>

Solving Systems of Linear Equations

Multivariable Calculus Practice Tests

A tutor can equip your student with plenty of math tricks, including working with vectors and much more. Varsity Tutors carefully vets each tutor, ensuring that your student always works alongside someone who truly understands these concepts. If your student isn''t clear about cross-multiplying and other important concepts covered in class, they can ask as many questions as they like during these 1-on-1 sessions. Reach out today, and Varsity Tutors will match your student with a suitable tutor.

Subjects Near Me

- Series 27 Courses & Classes
- Integrated Math 3 Tutors
- IB Diploma Essay Editing Tutors
- TACHS Courses & Classes
- Series 24 Test Prep
- CCNA Cyber Ops - Cisco Certified Network Associate-Cyber Ops Test Prep
- Series 79 Tutors
- New Jersey Bar Exam Courses & Classes
- New York Bar Exam Test Prep
- ABIM Exam - American Board of Internal Medicine Courses & Classes
- CLEP Introductory Business Law Test Prep
- CRISC - Certified in Risk and Information Systems Control Courses & Classes
- PANCE - Physician Assistant National Certifying Examination Test Prep
- CLEP Spanish Test Prep
- NBCOT - National Board of Certification in Occupational Therapy Tutors
- AIS - Associate in Insurance Services Courses & Classes
- Semiconductors Tutors
- Geometry Tutors
- Playwriting Tutors
- TOEFL Courses & Classes

Popular Cities