If `a=hat(i)+hat(j)+hat(k), b=2hat(i)+lambda hat(j)+hat(k), c=hat(i)-hat(j)+4hat(k)` and `a.(b xx c)=10`, then `lambda` is equal to

Options

A. 6
B. 7
C. 9
D. 10

Answer

A

Explanation

Given `a=hati+hatj+hatk, b=2hati+lamda hatj+hatk and c= hati-hatj+4 hatk`
Aslo, given `a*(bxx c)=10`
`implies|{:(1,1,1),(2 , lamda,1),(1,-1,4):}|=10`
`implies1(4lamda+1)-1(8-1)+1(-2-lamda)=10`
`implies 4 lamda +1-7-2-lamda=10`
`implies3 lamda =18 implieslamda =6`