A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
if vector A.B , does it necessarily follow that A = 0 or B = 0? explain
if vector AxB does it necessarily follow that A = 0 or B = 0? explain
anonymous
 one year ago
if vector A.B , does it necessarily follow that A = 0 or B = 0? explain if vector AxB does it necessarily follow that A = 0 or B = 0? explain

This Question is Open

VincentLyon.Fr
 one year ago
Best ResponseYou've already chosen the best response.0You mean: if A.B=0 ... if AxB=0 ... don't you?

LarsEighner
 10 months ago
Best ResponseYou've already chosen the best response.0If the dot product is zero, it does not imply that either of the vectors is 0. It implies the vectors are orthogonal. \( \mathbf{A} \cdot \mathbf{B} = \vert A \vert \vert B \vert \cos \theta \) where theta is the angle between them. If one of them were the zero vector, the dot product would also be zero because the zero vector is both perpendicular to and parallel with every other vector. The cross product of two vectors is a vector (unlike the dot product which is a number. \( \mathbf{A} \times \mathbf{B} = \vert A \vert \vert B \vert \sin \theta \mathbf n \) where n is a vector orthogonal to both A and B. it can be zero when sin theta is zero which happens when A and B are parallel or antiparallel (parallel in opposite directions). So if the dot product is zero or the cross product is the zero vector it is not necessarily true that either A or B is zero.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.