Vector Review

# The opposite direction magnitude of a vector the

• Notes
• 5

This preview shows page 2 - 4 out of 5 pages.

the opposite direction: Magnitude of a Vector: The Magnitude of a vector is also known as the “length” or “norm” of a vector. For vectors in R 3 , this is given by the Pythagorean Theorem: 2 2 2 z y x a a a a Unit Vectors:

Subscribe to view the full document.

A unit vector is a vector with a magnitude of one (that is, a vector with “unit length.”) A unit vector is often (but not always) denoted with a “hat” instead of an arrow. Unit vectors can be used to signify a direction. Given a vector ) , , ( z y x a a a a , we can find a unit vector that points in the same direction as a : 2 2 2 2 2 2 2 2 2 2 2 2 , , ) , , ( | | ˆ z y x z z y x y z y x x z y x z y x a a a a a a a a a a a a a a a a a a a a a We can compactly express the magnitude and direction of a vector by using the unit vector: a a a ˆ | | This reads: “the vector a has a magnitude | | a and points in the direction a ˆ .” Physics notation: We will use a (no arrow, plain type) instead of | | a . e.g. a a a ˆ A Very Special Unit Vector: The position vector ) , , ( z y x r is a vector from the origin to an arbitrary point in R 3 . The magnitude of the position vector is the distance from the origin to ( x,y,z) .

{[ snackBarMessage ]}

###### "Before using Course Hero my grade was at 78%. By the end of the semester my grade was at 90%. I could not have done it without all the class material I found."
— Christopher R., University of Rhode Island '15, Course Hero Intern

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern