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प्रश्न
If the scalar triple product of the vectors `-3hat"i" + 7hat"j" - 3hat"k", 3hat"i" - 7hat"j" + lambdahat"k" and 7hat"i" - 5hat"j" - 5hat"j"` is 272 then λ = ______.
पर्याय
9
11
8
0
MCQ
रिकाम्या जागा भरा
उत्तर
If the scalar triple product of the vectors `-3hat"i" + 7hat"j" - 3hat"k", 3hat"i" - 7hat"j" + lambdahat"k" and 7hat"i" - 5hat"j" - 5hat"j"` is 272 then λ = 11.
Explanation:
Scalar triple product of the given vectors is 272.
`therefore |(-3,7,-3),(3,-7,lambda),(7,-5,-3)|` = 272 (∵ scalar triple product of the vectors a, band c is [a b c])
⇒ -3(21 + 5λ) - 7(- 9 - 7λ) - 3(- 15 + 49) = 272
⇒ - 63 - 15λ + 63 + 49λ - 102 = 272
⇒ 34λ - 102 = 272
⇒ 34λ = 374
⇒ λ = 11
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