Question

Find the value of x + y from the following equation : 2 $\left(\begin{array}{l l }x & 5 \\ 7 & y-3\end{array}\right)$ + $\left(\begin{array}{l l }3 & -4 \\ 1 & 2\end{array}\right)$ = $\left(\begin{array}{l l }7 & 6 \\ 15 & 14\end{array}\right)$ .

For what values of $\stackrel{\rightarrow}{a}\$, the vectors $2\stackrel{\wedge}{i}-3\stackrel{\wedge}{j} +4\stackrel{\wedge}{k}$ and $a\,{\hat{\boldsymbol{i}}}+6\,{\hat{\boldsymbol{j}}}-8\,{\hat{\boldsymbol{k}}}$ are collinear?

Write the equation of tangent drawn to the curve y = sin x at the point (0, 0).

The elements $a_{i j}$ of a 3 × 3 matrix are given by $a_{i j}=\,\frac{1}{2}\,\vert-3i+j\vert.$. Write the value of element $a_{32}$.

Write the value of x - y + z from following equation. $\left(\begin{array}{l }x+y+z \\ x+z \\ y+z\end{array}\right)$ = $\left(\begin{array}{l }9 \\ 5 \\ 7\end{array}\right)$

If A' = $\left(\begin{array}{l l }3 & 4 \\ -1 & 2 \\ 0 & 1\end{array}\right)$ and B = $\left(\begin{array}{l l l }-1 & 2 & 1 \\ 1 & 2 & 3\end{array}\right)$ then find A' – B'.

Write a unit vector in the direction of the sum of vectors : $\stackrel{\rightarrow}{a}\ = 2\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +2\stackrel{\wedge}{k} and \stackrel{\rightarrow}{b}\ = \stackrel{\wedge}{i}+\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$