Question

If matrix A = [1 2 3], then write AA’.

Find the position vector of a point which divides the join of points with position vectors $\;\stackrel{\rightarrow}{(a}-2\stackrel{\rightarrow}{b})$ and $\;\stackrel{\rightarrow}{(2a}+\stackrel{\rightarrow}{b})$ externally in the ratio 2 : 1.

If $\begin{vmatrix}x+1 & x-1 \\ x-3 & x+2\end{vmatrix}$ = $\begin{vmatrix}4 & -1 \\ 1 & 3\end{vmatrix}$ , then write the value of x.

Evaluate: $\textstyle\int(1-x){\sqrt{x}}\,d x~.$

Evaluate $\textstyle\int$ sec² (7 – 4x) dx.

Evaluate $\textstyle\int$ sin³ x dx.

Find the differential equation of the family of lines passing through the origin.