Question

If $\left(\begin{array}{l l l }1 & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & 1\end{array}\right)$ $\left(\begin{array}{l }x \\ -1 \\ z\end{array}\right)$ = $\left(\begin{array}{l }1 \\ 2 \\ 1\end{array}\right)$ , find x + y + z.

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}\$

Write fog, if f : R → R and g : R → R are given by f(x) = |x| and g(x) = |5x - 2|.

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 2 $\left(\begin{array}{l l }1 & 3 \\ 0 & x\end{array}\right)$ + $\left(\begin{array}{l l }y & 0 \\ 1 & 2\end{array}\right)$ = $\left(\begin{array}{l l }5 & 6 \\ 1 & 8\end{array}\right)$ , write the value of (x + y).

If A, B and C are the vertices of a $\Delta A B C$, then what is the value of ${\vec{AB}}+{\vec{BC}}+{\vec{C A}}$ ?

Find a unit vector in the direction of $\stackrel{\rightarrow}{A}$ = $3\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +6\stackrel{\wedge}{k}$