Question

Give an example of vectors $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$ such that $\vert{\vec{b}}\vert=$ $\vert{\vec{b}}\vert$ but $\stackrel{\rightarrow}{a}\neq \stackrel{\rightarrow}{b}\;.$  

If a unit vector $\stackrel{\rightarrow}{a}\$ makes an angle $\frac{\pi}{3}$ with $\stackrel{\wedge}{i},$ $\frac{\pi}{4}$ with $\stackrel{\wedge}{j}$ and an acute angle θ with $\stackrel{\wedge}{k}$, then find the value of θ.

If $\begin{vmatrix} 2x & x+3 \\ 2(x+1) & x+1 \end{vmatrix} = \begin{vmatrix} 1 & 5 \\ 3 & 3 \end{vmatrix}$, write the value of x.

Find : $\int{\frac{3\,x}{3\,x-1}}\,d x$

If A = $\left(\begin{array}{l l }3 & 10 \\ 2 & 7\end{array}\right)$ , then write A⁻¹.

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

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