1 / 17

Vectors

Vectors. Scalars & Vectors. Vectors Quantity with both magnitude & direction Does NOT follow elementary arithmetic/algebra rules Examples – position, force, moment, velocities, acceleration. Magnitude. Head. Direction/Angle. Tail. Line of Action. Parallelogram Law.

aliza
Télécharger la présentation

Vectors

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Vectors

  2. Scalars & Vectors • Vectors • Quantity with both magnitude & direction • Does NOT follow elementary arithmetic/algebra rules • Examples – position, force, moment, velocities, acceleration Magnitude Head Direction/Angle Tail Line of Action

  3. Parallelogram Law • The resultant of two forces can be obtained by • Joining the vectors at their tails A A+B • Constructing a parallelogram B • The resultant is the diagonal of the parallelogram

  4. Triangle Construction • The resultant of two forces can be obtained by • Joining the vectors in tip-to-tail fashion A B R • The resultant extends from the tail of A to the head of the B

  5. Vector Addition • Does A + B = B + A ? A B R R A B YES! - commutative

  6. Vector Subtraction A-B = A + (-B) A -B B -B R A

  7. Vector Subtraction • Does A – B = B - A ? -B B R -R A -A NO! – opposite sense

  8. Vector Operations • Multiplication & Division of Vector (A) by Scalar (a) a * A = aA 2A 2 * A = 2A A -.5 * A = -.5A A -.5A

  9. Representation of a Vector Given the points and , the vector a with representation is a Find the vector represented by the directed line segment with initial point A(2,-3,4) and terminal point B(-2,1,1).

  10. Magnitude of a vector Determine the magnitude of the following:

  11. Example

  12. Parallel • Two vectors are parallel to each other if one is the scalar multiple of the other. Determine if the two vectors are parallel These are parallel since b= -3a These are not parallel since 4(1/2) =2 , but 10(1/2)=5 not -9

  13. Unit vectors Any vector that has a magnitude of 1 is considered a unit vector. Can you think of a unit vector?

  14. Standard Basis Vectors Example- Write in terms of the standard basis vector i,j,k.

  15. Example If a = i + 2j - 3k and b = 4i + 7k, express the vector 2a+3b in terms of i,j,k. 2a+3b=2(i + 2j - 3k)+3(4i + 7k) 2a+3b=2i + 4j - 6k+ 12i + 21k 2a+3b=14i+4j+15k

  16. Unit Vectors The unit vector in the same direction of a is Find a unit vector in the same direction as 2i – j – 2k. We are looking for a vector in the same direction as the original vector, but is also a unit vector. Let’s first find the magnitude Check? Same direction? Magnitude = 1?

  17. Homework • P649 • 4,5,7,9,11,15,17,19

More Related