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
DifficultIf the points with position vectors $60 \hat{i}+3 \hat{j}$,$40 \hat{i}-8 \hat{j}$,and $a \hat{i}-52 \hat{j}$ are collinear,then $a$ is equal to
- A$-40$
- B$-20$
- C$20$
- D$40$
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Similar Questions
The solutions of $\operatorname{det}(A-\lambda I_2)=0$ are $4$ and $8$, where $A=\begin{bmatrix} 2 & 3 \\ x & y \end{bmatrix}$. Then:
Find the values of $k$ if the area of the triangle is $4$ square units and the vertices are $(k, 0), (4, 0), (0, 2)$.
Medium
View SolutionIf the system of equations $2x + 3y - z = 0$,$x + ky - 2z = 0$ and $2x - y + z = 0$ has a non-trivial solution $(x, y, z)$,then $\frac{x}{y} + \frac{y}{z} + \frac{z}{x} + k$ is equal to
DifficultJEE MAIN 2019
View SolutionThe value of $a$ for which the matrix $A = \begin{bmatrix} a & 2 \\ 2 & 4 \end{bmatrix}$ is singular is:
Easy
View SolutionIf $\left|\begin{array}{ccc}\cos (A+B) & -\sin (A+B) & \cos (2 B) \\ \sin A & \cos A & \sin B \\ -\cos A & \sin A & \cos B\end{array}\right|=0$,then the value of $B$ is
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