Question

Whether x+4y-z=7 & 5x-3y-7z+11 are orthogonal, parallel?

Answer 1

check if
\[<1,4,-1>\]is proportional to \[<5,-3,11>\]

Answer 2

which clearly it is not since one is not a multiple of the other
not parallel

Answer 3

to see if they are perpendicular, check the dot product
if it is zero then are "orthogonal"

Answer 4

you know how to compute the dot product?

Answer 5

how to solve it?

Answer 6

\[<x_1,x_2,x_3>\cdot<y_1,y_2,y_3>=x_1y_1+x_2y_2+x_3y_3\]

Answer 7

i.e multiply and add

Answer 8

it's 0, that means it is orthogonal

Answer 9

yes

Answer 10

thank you satellite 73!

Answer 11

matrix A=[1 2 5: 2 -1 3: 1 1 -1] how to find A^2 =AA?

Answer 12

grind it till you find it

Answer 13

matrix multiplication is not something i can write here
i would use a computer anyway, it is donkey work

Answer 14

http://www.wolframalpha.com/input/?i=matrix+multiplication+calculator&f1= {{1%2C2%2C5}%2C{2%2C-1%2C3}%2C{1%2C1%2C-1}}&f=MatricesOperations.theMatrix1_{{1%2C2%2C5}%2C{2%2C-1%2C3}%2C{1%2C1%2C-1}}&f2={{1%2C2%2C5}%2C{2%2C-1%2C3}%2C{1%2C1%2C-1}}&f=MatricesOperations.theMatrix2_{{1%2C2%2C5}%2C{2%2C-1%2C3}%2C{1%2C1%2C-1}}&a=*FVarOpt.1-_**-.***MatricesOperations.theMatrix3---.*--

Answer 15

hi satellite 73 I couldn't open your link to solve matrix