Question

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 = ______.

Options

• 9

• 11

• 8

• 0

Answer 1

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