If 1 i 2- m i 2- n i 2-1 for i -1-2-3 - l i l j - m i m j - n i n j -0 for i - j -1-2-3 and i - j and Delta - beginvmatrix 1- 18 m - 1 - n - 1l2 - m - 2 - n - 2 11- 3 - m - 3 - n - 3lend vmatrix - thenA- -3B- -2C- -1D- -0

The correct option is C |Δ| =1Δ^2 = l_1 amp; m_1 amp; n_1 nbsp; l_2 amp; m_2 amp; n_2 nbsp; l_3 amp; m_3 amp; n_3 l_1 amp; l_2 ...

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Evaluation of a Determinant

If 1 i 2+ m i...

Question

If $l_{i}^{2} + m_{i}^{2} + n_{i}^{2} = 1$ for $i = 1, 2, 3$ & $l_{i} l_{j} + m_{i} m_{j} + n_{i} n_{j} = 0$ for $i, j \in {1, 2, 3}$ and $i \neq j$ and $Δ = ∣ ∣ ∣ ∣ \begin{matrix} l_{1} & m_{1} & n_{1} l_{2} & m_{2} & n_{2} l_{3} & m_{3} & n_{3} \end{matrix} ∣ ∣ ∣ ∣,$ then

| Δ | = 3

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| Δ | = 2

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| Δ | = 1

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| Δ | = 0

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Solution

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Similar questions

l_{i}^{2} + m_{i}^{2} + n_{i}^{2} = 1

i = 1, 2, 3

l_{i} l_{j} + m_{i} m_{j} + n_{i} n_{j} = 0

i, j \in {1, 2, 3}

i \neq j

Δ = ∣ ∣ ∣ ∣ \begin{matrix} l_{1} & m_{1} & n_{1} l_{2} & m_{2} & n_{2} l_{3} & m_{3} & n_{3} \end{matrix} ∣ ∣ ∣ ∣,

l_{i}^{2} + m_{i}^{2} + n_{i}^{2} = 1

l_{i} l_{j} + m_{i} m_{j} + n_{i} n_{j} = 0

i \neq j

i, j \in {1, 2, 3}

A = ⎡ ⎢ ⎣ \begin{matrix} l_{1} & m_{1} & n_{1} l_{2} & m_{2} & n_{2} l_{3} & m_{3} & n_{3} \end{matrix} ⎤ ⎥ ⎦, then | A | =

a > b > 0

I (n) = a^{1 / n} - b^{1 / n},

J (n) = (a - b)^{1 / n}

n \geq 2

I (m) = \int_{0}^{1} x^{m} . ln x d x

J (m) = \int_{0}^{1} x^{m} . (ln x)^{2} d x

m \in N,

[lim x \to 0 \frac{sin x}{x}] = 0

x \in (- δ, δ)

δ

δ \to 0, tan x > x .

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