Question

given v=5i-2j and w=-3i+j, find v * w

Answer 1

use ther properties of complex number

Answer 2

?

Answer 3

\(v=5i-2j\) and \(w=-3i+j\)

\[ v \times w=(5i-2j)\times(-3i+j)\]

Answer 4

wait,
does * indicate the dot or cross product?

Answer 5

HMMM

Answer 6

or does it indicate simple multiplication where you use FOIL?

Answer 7

hey dork, is it dot or cross product?

Answer 8

:)

Answer 9

@chaise Nope.. it looks like vectors

Answer 10

yes its vectors

Answer 11

is it dot product or cross product (third time of this question..) ???

Answer 12

dot?

Answer 13

v (dot) w =(5)(-3) + (-2)(1) = ... ?

Answer 14

yes

Answer 15

wait

Answer 16

im confused now xD

Answer 17

\(v = x_1i+y_1j\) and \(w= x_2i+y_2j\)

v (dot) w = \(x_1x_2 + y_1y_2\)

Answer 18

given that they are 2 non-zero vectors

Answer 19

\[v=5i-2j=(-3,-2)\]
\[w=-3i+j=(-3,1)\]

\[v \cdot w=(5,-2)\cdot(-3,+1)\]\[\qquad=\left(5\times-3,\quad-2\times1\right)\]

Answer 20

Convert the complex numbers to exponential form and use
\[z _{1}z _{2}=r _{1}r _{2}e ^{i(\theta _{1}+\theta _{2})}\]

Answer 21

what complex numbers?

Answer 22

\[\{\hat i,\hat j\}\] are the unit vectors in the x, y dircetions

Answer 23

Good question. j is used instead of i in electrical engineering.

Answer 24

Given two non-zero vectors \(v = x_1i+y_1j\) and \(w = x_2i+y_2j\)
\[v \cdot w = (x_1i+y_1j) \cdot (x_2i+y_2j)\]\[v \cdot w = x_1i\cdot (x_2i+y_2j)+y_1j \cdot (x_2i+y_2j)\]\[v \cdot w = x_1x_2i\cdot i+x_1y_2i\cdot j+y_1x_2i\cdot j+y_1y_2j\cdot j\]\[v \cdot w = x_1x_2+0+0+y_1y_2\]\[v \cdot w = x_1x_2+y_1y_2\]

Note that \(i \cdot i = 1\) and \(i\cdot j = 0\)