If p- begin vmatrix - 81111 -xlend vmatrix and Q - vmatrix X - 1 - 11 l1 - x - 111181 - xend vmatrix then dQ - dx -A- 3 P -1B- 1-3 PC- -3 PD- 3 P

The correct option is D 3P dQ/dx= 1 amp; 0 amp; 0 1 amp; x amp; 1 1 amp; 1 amp; x + x amp; 1 amp; 1 0 amp; 1 amp; 0 1 am ...

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Byju's Answer

Standard XII

Mathematics

Applications of Cross Product

If p= begin v...

Question

If $p = ∣ ∣ ∣ \begin{matrix} x & 1 1 & x \end{matrix} ∣ ∣ ∣$ and $Q = ∣ ∣ ∣ ∣ \begin{matrix} x & 1 & 1 1 & x & 1 1 & 1 & x \end{matrix} ∣ ∣ ∣ ∣$ then $\frac{d Q}{d x}$ =.......

3P+1

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1-3P

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-3P

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Solution

The correct option is D
3P

$\frac{d Q}{d x} = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 0 & 0 1 & x & 1 1 & 1 & x \end{matrix} ∣ ∣ ∣ ∣ + ∣ ∣ ∣ ∣ \begin{matrix} x & 1 & 1 0 & 1 & 0 1 & 1 & x \end{matrix} ∣ ∣ ∣ ∣ + ∣ ∣ ∣ ∣ \begin{matrix} x & 1 & 1 1 & x & 1 0 & 0 & 1 \end{matrix} ∣ ∣ ∣ ∣ = 3 (x^{2} - 1) = 3 P$

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Similar questions

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P = ∣ ∣ ∣ \begin{matrix} x & 1 1 & x \end{matrix} ∣ ∣ ∣

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then

\frac{d Q}{d x} =

If $p = ∣ ∣ ∣ \begin{matrix} x & 1 1 & x \end{matrix} ∣ ∣ ∣$ and $Q = ∣ ∣ ∣ ∣ \begin{matrix} x & 1 & 1 1 & x & 1 1 & 1 & x \end{matrix} ∣ ∣ ∣ ∣$ then $\frac{d Q}{d x}$ =.......

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P = ∣ ∣ ∣ \begin{matrix} x & 1 1 & x \end{matrix} ∣ ∣ ∣

and

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\frac{d Q}{d x} =

_____

Q. Prove that

∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 + p & 1 + p + q 2 & 3 + 2 p & 4 + 3 p + 2 q 3 & 6 + 3 p & 10 + 6 p + 3 q \end{matrix} ∣ ∣ ∣ ∣

= 1

Q. The value of

∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 + p & 1 + p + q 2 & 3 + 2 p & 4 + 3 p + 2 q 3 & 6 + 3 p & 10 + 6 p + 3 q \end{matrix} ∣ ∣ ∣ ∣

is:

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If p=∣∣∣x11x∣∣∣ and Q=∣∣ ∣∣x111x111x∣∣ ∣∣ then dQdx=.......

The correct option is D 3P dQdx=∣∣ ∣∣1001x111x∣∣ ∣∣+∣∣ ∣∣x1101011x∣∣ ∣∣+∣∣ ∣∣x111x1001∣∣ ∣∣=3(x2−1)=3P

If $p = ∣ ∣ ∣ \begin{matrix} x & 1 1 & x \end{matrix} ∣ ∣ ∣$ and $Q = ∣ ∣ ∣ ∣ \begin{matrix} x & 1 & 1 1 & x & 1 1 & 1 & x \end{matrix} ∣ ∣ ∣ ∣$ then $\frac{d Q}{d x}$ =.......