Question

If $\left(\begin{array}{l l }1 & 2 \\ 3 & 4\end{array}\right)$ $\left(\begin{array}{l l }3 & 1 \\ 2 & 5\end{array}\right)$ = $\left(\begin{array}{l l }7 & 11 \\ k & 23\end{array}\right)$ , then write the value of k.

Given $\textstyle\int e^{x}(\tan x+1)\sec x\,d x=e^{x}f(x)+c.$ Write f(x) satisfying the above.

Find the projection of vector $\stackrel{\rightarrow}{a}\$ = $2\stackrel{\wedge}{i}+3\stackrel{\wedge}{j} +2\stackrel{\wedge}{k}$ on the vector $\stackrel{\rightarrow}{b}\$ = $2\stackrel{\wedge}{i}+2\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$

If x $\left(\begin{array}{l }2 \\ 3\end{array}\right)$ + y $\left(\begin{array}{l }-y \\ y\end{array}\right)$ = $\left(\begin{array}{l }10 \\ 5\end{array}\right)$ , write the value of x.

If a line has direction ratios 2, – 1, – 2, then what are its direction cosines ?

The two vectors $:{\hat{j}}+{\hat{k}}$ and $3\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +4\stackrel{\wedge}{k}$ represent the two sides AB and AC, respectively of $\Delta A B C.$ Find the length of the median through A.

Evaluate $\textstyle\int\!{\frac{x^{3}-x^{2}+x-1}{x-1}}\,d x\,.$