If the scalar triple product of the vectors -3i^+7j^-3k^,3i^-7j^+λk^ and 7i^-5j^-3k^ is 272 then λ= …

Correct answer: (B) 11. Scalar triple product of the given vectors is 272. ∴ -3 7 -3 3 -7 λ 7 -5 -3 =272 ( ∵ scalar triple product of the vectors a, b and c is [a b c]) ⇒-321+5λ-7-9-7λ-3-15+49=272 ⇒-63-15λ+63+49λ-102=272 ⇒34λ-102=272 ⇒34λ=374 ⇒λ=11

Q58 / 150 · MHT CET 2019 (Shift 1) · Mathematics

If the scalar triple product of the vectors $- 3 \hat{i} + 7 \hat{j} - 3 \hat{k}, 3 \hat{i} - 7 \hat{j} + λ \hat{k}$ and $7 \hat{i} - 5 \hat{j} - 3 \hat{k}$ is 272 then $λ =$ …

A
9
Correct answer
B
11
C
8
D
10

Solution

Scalar triple product of the given vectors is 272.

∴ |\begin{matrix} - 3 & 7 & - 3 \\ 3 & - 7 & λ \\ 7 & - 5 & - 3 \end{matrix}| = 272

(

∵

scalar triple product of the vectors a, b and c is [a b c])

\Rightarrow - 3 (21 + 5 λ) - 7 (- 9 - 7 λ) - 3 (- 15 + 49) = 272

\Rightarrow - 63 - 15 λ + 63 + 49 λ - 102 = 272

\Rightarrow 34 λ - 102 = 272

\Rightarrow 34 λ = 374

\Rightarrow λ = 11

Hence, the correct answer is option: 'B'.

If the scalar triple product of the vectors -3i^+7j^-3k^,3i^-7j^+λk^ and 7i^-5j^-3k^ is 272 then λ= …

Solution

Relevant Questions

If the scalar triple product of the vectors $- 3 \hat{i} + 7 \hat{j} - 3 \hat{k}, 3 \hat{i} - 7 \hat{j} + λ \hat{k}$ and $7 \hat{i} - 5 \hat{j} - 3 \hat{k}$ is 272 then $λ =$ …