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ApoorvGoel · Apr 6, 2011, 10:13 AM

If the position vectors (-jcap-kcap), (4icap+5jcap+lambdakcap), (3icap+9jcap+4kcap) and (-4icap+4jcap+4kcap)are coplanar, than the value of lambda is
1. -1
2. 0
3. 1
4. 2

please give your choice with explanation
please specify that what is the condition of coplanar...

galactus · Apr 7, 2011, 05:39 AM

$A=(0,-1,-1), \;\ B=(4,5,L), \;\ C=(3,9,4), \;\ D=(-4,4,4)$

$AB=-4i-6k+(-L-1)k$

$AC=-3i-10j-5k$

$AD=4i-5j-5k$

Cross Product:

$AC\times AD=25i-35j+55k$

Dot product of ACxAD and AB

$\begin{vmatrix}25&-35&55\\-4&-6&-L-1\end{vmatrix}=55-55L$

The dot product is 0 if they are coplanar.

$55-55L=0\Rightarrow L=1$

ApoorvGoel · Apr 7, 2011, 09:37 AM

Thanks a lot for your answer