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Lecture 3

Operations on vectors (Algebra):

Addition: use the tip to tail method

Multiplication by -1

o Flip the vector so that it goes the exact opposite way with the same starting point

Multiplication by any number (scalar), x

o If the scalar is positive:

Multiply the length of the vector by the scalar

o If the scalar is negative:

Multiply the length of the vector by the absolute value of the scalar, and

then multiply that by -1

Subtraction

o Multiply the vector being subtracted by -1 and then add that to the preexisting

vector

Algebra using coordinates:

o All vectors can be made up by the vectors i = <1, 0, 0>, j = < 0, 1 , 0>,

and k = < 0, 0, 1>

o Any vector u = xi + yj + zk

o For example: u = <1, 4, 2> = i + 4j + 2k

Magnitude of vector u:

o

Definition: a unit vector is a vector u with magnitude 1

Ex) u = <

=

= 1

Ex) u = <-2, 1, 5>

=

The unit vector is <

>

Definition: If the vector u = <x, y, z>

Then the vector u multiplied by the scalar A = <Ax, Ay, Az>

Ex) A =

and the vector u = <-2, 1, 5>

Au = <

>

Remark: If A = (XA, YA, ZA) and B = (XB, YB, ZB)

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