If scalar triple product of vectors -k- 3 -4 -5 k- 7 -2 -11 k- is given by the determinant - a1 a2 a3- b1 b2 b3- c1 c2 c3 - then a1-b2-c3-

Let’s say we have 3 vectors a_1î+a_2ĵ+a_3k̂ b_1î+b_2ĵ+b_3k̂ c_1î+c_2ĵ+c_3k̂ Th ...

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Scalar Triple Product

If scalar tri...

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If scalar triple product of vectors $^i +^j +^k, 3^i + 4^j + 5^k, 7^i + 2^j + 11^k$ is given by the determinant $∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} b_{1} & b_{2} & b_{3} c_{1} & c_{2} & c_{3} \end{matrix} ∣ ∣ ∣ ∣$ then $a_{1} + b_{2} + c_{3} =$ __.

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^i +^j +^k, 3^i + 4^j + 5^k, 7^i + 2^j + 11^k

∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} b_{1} & b_{2} & b_{3} c_{1} & c_{2} & c_{3} \end{matrix} ∣ ∣ ∣ ∣

a_{1} + b_{2} + c_{3} =

\to a = 3^i + 4^j - 5^k

|^i \times (\to a \times^i) +^j \times (\to a \times^j) +^k \times (\to a \times^k) | =

2^i -^j +^k,^i + 2^j - 3^k

3^i + λ^j + 5^k

λ =

^i +^j +^k,^i + 3^j + 5^k, 7^i + 9^j + 11^k

\to a =^i + 2^j +^k, \to b = 2^i +^j

\to c = 3^i - 4^j - 5^k

(\to a - \to b)

(\to c - \to b)

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