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Question
If `overlinea = 3hati + hatj + 4hatk, overlineb = 2hati - 3hatj + lambdahatk, overlinec = hati + 2hatj - 4hatk` and `overlinea.(overlineb xx overlinec) = 47`, then λ is equal to ______
Options
4
5
6
7
MCQ
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Solution
If `overlinea = 3hati + hatj + 4hatk, overlineb = 2hati - 3hatj + lambdahatk, overlinec = hati + 2hatj - 4hatk` and `overlinea.(overlineb xx overlinec) = 47`, then λ is equal to 5.
Explanation:
`overlinea.(overlineb xx overlinec) = 47`
∴ `|(3, 1, 4), (2, -3, lambda), (1, 2, -4)| = 47`
⇒ 3(12 - 2λ) - 1(-8 - λ) + 4(4 + 3) = 47
⇒ λ = 5
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