Statement 1: `vecA=2hati + 3hatj + 6hatk , vecB=hati + hatj - 2hatk and vecC=hati + 2hatj + hatk` then
`|vecAxx (vecAxx(vecAxxvecB)).vecC|= 243`
Statement 2: `|vecAxx(vecAxx(vecAxxvecB)).vecC|=|vecA|^(2)|[vecA vecB vecC]|`

Options

A. A. Both the statements are true and statement 2 is the correct explanation for statement 1.
B. B. Both statements are true but statement 2 is not the correct explanation for statement 1.
C. C. Statement 1 is true and Statement 2 is false
D. D. Statement 1 is false and Statement 2 is true.

Answer

d

Explanation

`vecA xx (vecA.vecB) vecA- (vecA.vecA) vecB) .vecC`
`(=underset("zero")ubrace(vecAxx(vecA.vecB)vecA)-(vecA.vecA)xxvecB).vecC`
`=-|vecA|^(2)[vecA vecB vecC]`
now ` |vecA|^(2) = 4+9 + 36 = 49`
`[vecA vecB vecC]=|{:(2,3,6),(1,1,-2),(1,2,1):}|`
2( 1+4) -1 (3 -12) +1 (-6-6)
= 10 +9 -12 =7
`|vecA|^(2) [vecAvecBvecC]|= 49xx 7 = 343`