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If the line $\frac{\text{x}-3}{2}=\frac{\text{y}+2}{-1}=\frac{\text{z}+4}{3}$ lies in the plane lx + my - z = 9, then find the value of l2 + m2.
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Evaluate:
$\int\limits^{1}_{-2} \big|\text{x}^{3} - \text{x}\big| \text{ dx}$
→$\int\limits^{1}_{-2} \big|\text{x}^{3} - \text{x}\big| \text{ dx}$
Let A $=\begin{bmatrix}1&-2&1\\-2&3&1\\1&1&5\end{bmatrix}.$ Verify that
→- [adj. A]-1 = adj.(A-1)
- (A-1)-1 = A
Find the equation of the plane which contains planes is the line of intersection of the planes x + 2y + 3z - 4 = 0 and 2x + y - z + 5 = 0 and whose x-intercept is twice its z-intercept.
Find the coordinate of the point P where the line through $\text{A(3, – 4, –5) and B (2, –3, 1)}$ crosses the plane passing through three points L(2, $\text{2, 1), M(3, 0, 1) and N(4, –1, 0).}$ Also, find the ratio in which P divides the line segment AB.
→Solve the matrix equations:
$\begin{bmatrix}\text{x}&1\end{bmatrix}\begin{bmatrix}1&0\\-2&-3\end{bmatrix}\begin{bmatrix}\text{x}\\5\end{bmatrix}=0$
→$\begin{bmatrix}\text{x}&1\end{bmatrix}\begin{bmatrix}1&0\\-2&-3\end{bmatrix}\begin{bmatrix}\text{x}\\5\end{bmatrix}=0$