Chap 6

Question

Chap 6

eric_d · Answer

http://prntscr.com/4p67yk

eric_d · Answer

Question 7)

ikram002p · Answer

ok what have u tried so far ?

eric_d · Answer

I don't know how to begin...

eric_d · Answer

Can you guide me..

ganeshie8 · Answer

maybe for writing sake, say those $\lambda $'s are   x,y,z...

ikram002p · Answer

$\large s=-3i-j+6k=\lambda_1p+\lambda_2q+\lambda_3r \=\lambda_1(-i+2j+3k)+\lambda_2(3i+j-2k)+\lambda_3(i+5j+2k)$

ikram002p · Answer

$\lambda 's$ are values , so if u have a vector  $v=v_1i+v_2j+v_3k$
then $\lambda v =\lambda v_1i+\lambda v_2j+ \lambda v_3k$

ganeshie8 · Answer

next compare components both sides

ganeshie8 · Answer

$$-3i-j+6k=\lambda_1(-i+2j+3k)+\lambda_2(3i+j-2k)+\lambda_3(i+5j+2k)$$

ganeshie8 · Answer

whats the coefficient of $\large  i$ on left hand side ?

eric_d · Answer

-3

ganeshie8 · Answer

whats the coefficient of $\large i$ on right hand side ?

eric_d · Answer

There are three values for $i$ : -1,3,1

ganeshie8 · Answer

what about $\lambda $'s ? they are also attached to them right ?

ikram002p · Answer

i is the unit vector (1,0,0)
hmm

ganeshie8 · Answer

$$-3i-j+6k=\lambda_1(-i+2j+3k)+\lambda_2(3i+j-2k)+\lambda_3(i+5j+2k) $$

$$-3\color{Red}{i}-\color{Red}{j}+6\color{Red}{k} = \color{red}{i} (-\lambda_1 + 3\lambda_2 + \lambda_3) + \color{Red}{j}(2\lambda_1 + \lambda_2 + 5\lambda_3) + \color{Red}{k}(3\lambda_1 -2\lambda_2 + 2\lambda_3)$$

ganeshie8 · Answer

Now compare, 
you will get 3 equations and you can solve the 3 unknowns

ganeshie8 · Answer

$\large   -3 = -\lambda_1 + 3\lambda_2 + \lambda_3$

$\large   -1 = 2\lambda_1 + \lambda_2 + 5\lambda_3$

$\large   6 = 3\lambda_1 -2\lambda_2 + 2\lambda_3$

ganeshie8 · Answer

solve those 3 equations using any of your favorite methods

eric_d · Answer

How do I solve them .. using elimination method ?
@ganeshie8

ganeshie8 · Answer

that works

eric_d · Answer

ok

eric_d · Answer

Is there any simpler method..

ganeshie8 · Answer

you should get : http://www.wolframalpha.com/input/?i=solve++-3+%3D+-x+%2B+3y+%2B+z%2C+-1+%3D+2x+%2B+y+%2B+5z%2C6+%3D+3x+-2y+%2B+2z

ganeshie8 · Answer

i have used x,y,z instead of lambdas

ganeshie8 · Answer

I don't think there will be any simpler method this time :) you will have to solve those 3 equations and get above answer

eric_d · Answer

OK

eric_d · Answer

Thank you @ikram002p  and @ganeshie8

ikram002p · Answer

np :)