Practicing Success
If $\vec a,\vec b,\vec c$ are non-coplanar vectors and λ is a real number, then $[λ(\vec a+\vec b),λ^2\vec b,λ\vec c]=[\vec a,\vec b+\vec c,\vec b]$ for. |
No value of λ Exactly one value of λ Exactly two values of λ Exactly three values of λ |
No value of λ |
L.H.S. $[λ(\vec a+\vec b)×λ^2\vec b].λ\vec c=λ^4[(\vec a+\vec b)×\vec b].\vec c=λ^4[\vec a\,\vec b\,\vec c]$ R.H.S:=$\vec a×(\vec b+\vec c)]\vec b=[\vec a\,\vec c\,\vec b]=-[\vec a\,\vec b\,\vec c]$ $⇒λ^4[\vec a\,\vec b\,\vec c]=-[\vec a\,\vec b\,\vec c]$ $⇒λ^4=-1$ which is not possible |