Question

If $a=(1,2,3),b=(2,−1,1),c=(3,2,1)$ and $a×(b×c)=Î\pm a+βb×γc$ then

• A. $Î\pm =1,β=10,γ=3$
• B. $Î\pm =0,β=10,γ=−3$
• C. $Î\pm +β+γ=8$
• D. $Î\pm =β=γ=0$

Answer 1

Answer: (B)

Given,
$a=(1,2,3)=i+2j+3k$
$b=(2,−1,1)=2i−j+k$
and $c=(3,2,1)=3i+2j+k$
Now, $a×(b×c)=Î\pm a+βb+γc$
$⇒(aâ‹\dots c)b−(aâ‹\dots b)c=Î\pm a+βb+γc$
$⇒\{(i+2j+3k)â‹\dots (3i+2j+k)\}b$
$−\{(i+2j+3k)â‹\dots (2i−j+k)\}c$
$=Î\pm a+βb+γc$
$⇒(3+4+3)b−(2−2+3)c=Î\pm a+βb+γc$
$⇒0a+10b−3c=Î\pm a+βb+γc$
On comparing, we get
$Î\pm =0,β=10\text{ and }γ=−3$