# Vectors

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 specify that what is the condition of coplanar...

 galactus Posts: 2,272, Reputation: 1436 Ultra Member #2 Apr 7, 2011, 06:39 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 Posts: 36, Reputation: 10 Junior Member #3 Apr 7, 2011, 10:37 AM
Comment on galactus's post
Quote:
 Originally Posted by galactus $A=(0,-1,-1), \;\ B=(4,5,L), \;\ C=(3,9,4), \;\ D=(-4,4,4)$ $AB=-4i-6k+(-L-1)k$ $AC=-3i-10j-5k$ $AD=4i-5j-5k$ 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. $55-55L=0\Rightarrow L=1$

## Check out some similar questions!

Assume that a and b are two vectors in R^3 with the property that a*x = b*x For every vector x in R^3. Must a = b? If so, prove it. If not, give a Counterexample. What is this question asking?