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

Question

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

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

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - A
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`

5 views Answered 2023-02-05 15:29