Question

Hello. I need some helo

There are two vectors: a and b
\[a(-\frac{ k \sqrt{3} }{2};\frac{ k }{ 2 };k \sqrt{2})\]
\[b(\frac{ k \sqrt{3} }{2};\frac{ k }{ 2 };k \sqrt{2})\]
k>0 do i need to find k (according to hat they are lineraly) ?

Answer 1

oh, i forgot the problem: I Need to find the angle between this two vectors!

Answer 2

Angle between two vectors \(\theta\)=
\[\theta =\cos^{-1} (\frac{ a.b}{|a||b|})\]
a. b = dot product
|a|=magnitude of a
|b|=magnitude of b
@Kamille Can you try?

Answer 3

what does it mean dot product?

Answer 4

Suppose you have
\[a=2i+3j+4k\]
\[b=1i+2j+4k\]
\[a.b=2\times3+3\times2+4\times4\]

Answer 5

Oh, okay so
\[a.b=(-\frac{ k \sqrt{3}}{ 2 })*(\frac{ k \sqrt{3}}{ 2 })+(\frac{ k }{ 2 })*(\frac{ k }{ 2 })+(k \sqrt{2})(k \sqrt{2})\]

Answer 6

sorry forwaiting, it is still really hard for me to use LATEX :/

Answer 7

No problem, take your time :) You are doing good

Answer 8

|a|=\[|a|=\sqrt{(-\frac{ k \sqrt{3} }{ 2 })^{2}+(\frac{ k }{ 2 })^{2}+(k \sqrt{2})^{2}}\]

Answer 9

is it right?

Answer 10

Absolutely :)

Answer 11

thank you for your help! I have understood it now;)

Answer 12

Welcome :)