badge image

Enroll For Free Now & Improve Your Performance.

×
User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 11

                        

where and when should we use dot and cross product and why?

5 years ago

Answers : (1)

Latika Leekha
askIITians Faculty
165 Points
							Hello student,
It is extremely important to know the difference between dot and cross products and their usage.
We define the dot product of two vectors
r = ai + bj and s = ci + dj
to be r . s = ac + bd
Cross-product of two vetcors a and b is defined as
(ax, ay, az) X (bx, by, bz) = aybz - azby, azbx - axbz,axby - aybx = ||a||||b|| sin θ n
where n is the unit vector normal to a and b.
  • The dot product of two vectors is a number and not a vector.
  • The dot product represents vector similarity with a single number:
(ax, ay, az).(bx, by, bz) = axbx + ayby + azbz = ||a||||b|| cos θ
  • The dot product just measures the similarity as it only considers the interactions in matching dimensions. Hence, it can be stated to be a simple calculation with 3 components.
  • The cross-product takes into consideration the cross interactions. So, whenever you need interaction between differnet dimensions, you should use cross-product.
  • eg: Area is formed by vectors which point in varied directions. Hence, cross-product is used to emasure the area formed by two 3-d vectors.
  • Some of the instances where cross-product is used are:
  1. Find the direction perpendicular to two given vectors.
  2. Find the signed area spanned by two vectors.
  3. To figure out if two vectors are orthogonal
  4. “Multiply” two vectors when only perpendicular cross-terms make a contribution.
5 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 19 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details