Question

a=<3,0,-1>, find a vector b such that comp(sub a) b=2.

Answer 1

\[comp _{a}b=\frac{ a.b }{ |a| }\]

Answer 2

comp=2, so I made a vector b=<a,b,c> 2=(3a-c)/sqrt(10), now what?

Answer 3

\[
b=<0,1,-2\sqrt{10}>\\
a.b = 2\sqrt{10}\\
|a|=\sqrt{10}\\

\]

Answer 4

\[\frac { a. b} {|a|}=\frac { 2 \sqrt{10}} {\sqrt{10}}=2
\]

Answer 5

Did you understand it?

Answer 6

where did you get the values for b?

Answer 7

@eliassaab I understand how you get to a.b=2sqrt(10) but now how you get those values for vector b

Answer 8

I reread the question, i guess there are many other vectors, so you just pick them as long as they get to 2sqrt(10) by a.b

Answer 9

There infinitely many vectors that satisfy your condition. I guessed it.\[

|a|=\sqrt {10}\\
a. b = 2 \sqrt {10}

\]
you find b so that the last equation holds.

Answer 10

You could have taken \[b=<0, 100, -2\sqrt{10}>\]

Answer 11

got it, thanks

Answer 12

yw