Question

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

If $\stackrel{\rightarrow}{a}\$and $\stackrel{\rightarrow}{b}\$ are two unit vectors such that $\stackrel{\rightarrow}{a}\$ +$\stackrel{\rightarrow}{b}\$ is also a unit vector, then find the angle between $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$

Find a vector in the direction of vector $2\stackrel{\wedge}{i}-3\stackrel{\wedge}{j} +6\stackrel{\wedge}{k}$which has magnitude 21 units.

Find : $\textstyle\int\!{\frac{1}{x(1+\log x)}}\,d x$

Write the value of x + y + z if $\left(\begin{array}{l l l }1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right)$ $\left(\begin{array}{l }x \\ y \\ z\end{array}\right)$ = $\left(\begin{array}{l }1 \\ -1 \\ 0\end{array}\right)$.

If $\left(\begin{array}{l l l }2 & 1 & 3\end{array}\right)$ $\left(\begin{array}{l l l }-1 & 0 & -1 \\ -1 & 1 & 0 \\ 0 & 1 & 1\end{array}\right)$ $\left(\begin{array}{l }1 \\ 0 \\ -1\end{array}\right)$ = A , then write the order of matrix A.

Write a vector in the direction of the vector $\displaystyle{\hat{\iota}}-2\,{\hat{\iota}}+2\,{\hat{\iota}}$ that has magnitude 9 units.