Question

Write a unit vector in the direction of the sum of vectors ${\vec{a}}{=}2\,\vec{i}+2\,\vec{j}-5\,\vec{k}\ \mathrm{~and}\ \vec{b}=2\,\vec{i}+\vec{j}-{7}\vec{k}.$

Write the projection of the vector $7\stackrel{\wedge}{i}+\stackrel{\wedge}{j} -4\stackrel{\wedge}{k}$ on the vector $2\stackrel{\wedge}{i}+6\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$.

Find matrix A such that. $\left(\begin{array}{l l}{2}&{-1}\\ {1}&{0}\\ {-3}&{4}\end{array}\right)$ $A={\left(\begin{array}{l l}{-1}&{-8}\\ {1}&{-2}\\ {9}&{22}\end{array}\right)}$

Using derivative, find the approximate percentage increase in the area of a circle if its radius is increased by 2%.

What is the range of the function f(x) = $\textstyle{\frac{|x-1|}{x-1}}$, x ≠ 1?

Find the matrix A if $\left(\begin{array}{l l l }9 & -1 & 4 \\ -2 & 1 & 3\end{array}\right)$ = A + $\left(\begin{array}{l l l }1 & 2 & -1 \\ 0 & 4 & 9\end{array}\right)$

If A = $\left(\begin{array}{l l}{{0}}&{{3}}\\ {{2}}&{{-5}}\end{array}\right)$ and $K A\ =\ {\left(\begin{array}{l l}{0}&{4a}\\ {-8}&{5b}\end{array}\right)}$ find the values of k and a.