Class 12Mathematics3 and 4 .Determinants and MatricesExpansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line
Easyयदि $\left|\begin{array}{ccc}1+x & 1 & 1 \\ 1+y & 1+2 y & 1 \\ 1+z & 1+z & 1+3 z\end{array}\right| = 10 k x y z \left(3+\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)$ है,तो $k = \text{ . . . . . . }$ (जहाँ $x, y, z \neq 0$ और $3+\frac{1}{x}+\frac{1}{y}+\frac{1}{z} \neq 0$).
- A$\frac{1}{5}$
- B$2$
- C$5$
- D$1$
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$A(k, 1)$,$B(2, 4)$ और $C(1, 1)$ शीर्षों वाले त्रिभुज का क्षेत्रफल $6$ वर्ग इकाई है। $k$ का मान ज्ञात कीजिए।
यदि $a \ne 6, b, c$ समीकरण $\left| \begin{array}{ccc} a & 2b & 2c \\ 3 & b & c \\ 4 & a & b \end{array} \right| = 0$ को संतुष्ट करते हैं,तो $abc = $
Easy
View Solutionमान लीजिए $A = \begin{bmatrix} 1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1 \end{bmatrix}$,जहाँ $0 \le \theta < 2\pi$,तो:
यदि $w = \frac{-1-i \sqrt{3}}{2}$ जहाँ $i = \sqrt{-1}$ है,तो $\left|\begin{array}{ccc}1 & w & w^2 \\ w & w^2 & 1 \\ w^2 & 1 & w\end{array}\right|$ का मान ज्ञात कीजिए।
सारणिक $\left| \begin{array}{ccc} a & b & a\alpha + b \\ b & c & b\alpha + c \\ a\alpha + b & b\alpha + c & 0 \end{array} \right| = 0$ है,यदि $a, b, c$ किसमें हैं?
MediumIIT 1986
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