Question

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

If f is an invertible function, defined as f(x) = $\frac{3x-4}{5}$, then write $f^{-1}(x).$

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 $\left(\begin{array}{l l }x-y & 2y \\ 2y+z & x+y\end{array}\right)$ = $\left(\begin{array}{l l }1 & 4 \\ 9 & 5\end{array}\right)$

Find $|\stackrel{\rightarrow}{x}|\$, if for a unit vector $\stackrel{\rightarrow}{a}\$ and ($\stackrel{\rightarrow}{x}\$ + $\stackrel{\rightarrow}{a}\$ )($\stackrel{\rightarrow}{x}\$ -$\stackrel{\rightarrow}{a}\$ ) = 15.

If $\begin{vmatrix}x+1 & x-1 \\ x-3 & x+2\end{vmatrix}$ = $\begin{vmatrix}4 & -1 \\ 1 & 3\end{vmatrix}$ , then write the value of x.

Find a vector in the direction of $\stackrel{\rightarrow}{a}=\stackrel{\wedge}{i}-2\;\stackrel{\wedge}{j}$ that has magnitude 7 units.