Select and write the appropriate answer from the given alternatives in each of the following sub- questions:
if `hata = 3hati - hatj + 4hatk, barb = 2hati + 3hatj - hatk, barc = - 5 hat i + 2hatj + 3hatk` then `bara . (barb xx barc)` = ……….

Options

A. 100
B. 101
C. 110
D. 109

Explanation

We have `bara = 3hati- hatj + 4hatk `
` barb = 2hatj + 3hatk + hatk`
`barc = - 5hati + 2hatj + 3 hatk`
`barb xx barc = |{:(hati , hatj ,hatk),(2,3,-1),(-5,2,3):}|`
`hati (9+ 2) - hatj (6-5)hatk + (4+ 5)`
`= 11 hati - hatj + 19hatk`
`bara.(barb xx barc) = (3hati- hatj + 4hatk).(11hati- hatjk + 19 hatk)`
` = 33 + 1 + 76`
= 110
Hence, the correct answer from the given alternatives is (c).