# Thread: Find K

1. ## Find K

Given

$\displaystyle \begin{vmatrix} b^2 + c^2 & ab & ac \\ ba & c^2+a^2 & bc \\ ca & cb & b^2+a^2 \end{vmatrix}$ = $\displaystyle \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix}$ = $\displaystyle K a^2 b^2 c^2$
Find K?

2. Originally Posted by zorro
Given

$\displaystyle \begin{vmatrix} b^2 + c^2 & ab & ac \\ ba & c^2+a^2 & bc \\ ca & cb & b^2+a^2 \end{vmatrix}$ = $\displaystyle \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix}$ = $\displaystyle K a^2 b^2 c^2$
Find K?
$\displaystyle \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix} = 0 \, ....$

3. Originally Posted by mr fantastic
$\displaystyle \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix} = 0 \, ....$
and

$\displaystyle \begin{vmatrix}b^2 + c^2 & ab & ac \\ba & c^2+a^2 & bc \\ca & cb & b^2+a^2 \end{vmatrix} = ... = 4a^2b^2c^2$

4. $\displaystyle \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix} = 2abc$

5. ## Whatz the answer

What is the Answer

6. Originally Posted by mr fantastic
$\displaystyle \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix} = 0 \, ....$
Originally Posted by Rapha
$\displaystyle \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix} = 2abc$
Whoops. My careless mistake. Thanks for the catch.

7. Originally Posted by zorro
What is the Answer
Look at post #3 and post #4 and draw the obvious conclusion.

8. Originally Posted by zorro
Given

$\displaystyle \begin{vmatrix} b^2 + c^2 & ab & ac \\ ba & c^2+a^2 & bc \\ ca & cb & b^2+a^2 \end{vmatrix}$ = $\displaystyle \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix}$ = $\displaystyle K a^2 b^2 c^2$
Find K?

I am getting some other answer........

$\displaystyle \begin{vmatrix} b^2 + c^2 & ab & ac \\ ba & c^2+a^2 & bc \\ ca & cb & b^2+a^2 \end{vmatrix}$ = $\displaystyle 3a^2b^2c^2 + a^2bc^3 + a^4bc$

and

$\displaystyle \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix}$ = $\displaystyle -a+2abc$

please tell me what i did wrong

9. Originally Posted by zorro
I am getting some other answer........

$\displaystyle \begin{vmatrix} b^2 + c^2 & ab & ac \\ ba & c^2+a^2 & bc \\ ca & cb & b^2+a^2 \end{vmatrix}$ = $\displaystyle 3a^2b^2c^2 + a^2bc^3 + a^4bc$

and

$\displaystyle \begin{vmatrix} 0 & c & b\\ c & 0 & a \\ b & a & 0 \end{vmatrix}$ = $\displaystyle -a+2abc$

please tell me what i did wrong
Can you explain hw you got those answers - the second one in particular ....

10. ## here my answer

$\displaystyle \begin{vmatrix} 0 & c & b \\ c & 0 & a \\ b & a & 0 \end{vmatrix}$=$\displaystyle 0(0-a)-c(0-ab)+b(ca-0)$=$\displaystyle -a+abc+abc$=$\displaystyle -a+2abc$

11. Originally Posted by zorro
$\displaystyle \begin{vmatrix} 0 & c & b \\ c & 0 & a \\ b & a & 0 \end{vmatrix}$=$\displaystyle 0(0-a)-c(0-ab)+b(ca-0)$ Mr F says: 0(0 - a) = 0.
=$\displaystyle -a+abc+abc$=$\displaystyle -a+2abc$
..