wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

What if the cross product is 0?


Open in App
Solution

Cross Product:

Cross product is a binary operation on two vectors in three-dimensional space. It results in a vector that is perpendicular to both vectors.

Formula: The vector product or cross product of two vectors A and B is A×B=|A||B|sinθn^

If the cross product of two vectors is 0, then

  • Both vectors are parallel to each other.
  • The angle between the vectors is 0.
  • One of them or both vectors are zero vectors.

Example: The cross product of two vectors A=i^+j^+k^ and B=2i^+2j^+2k^ is,

A×B=i^j^k^111222

A×B=1·2-2·1i^-1·2-2·1j^+1·2-2·1k^

A×B=2-2i^-2-2j^+2-2k^

A×B=0i^-0j^+0k^

A×B=0

Hence, if cross product of any two vectors is zero then vectors are parallel, one vector or both vectors are zero.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Application of Vectors - Lines
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon