Question

If A = $\left(\begin{array}{l l l }1 & 2 & 2 \\ 2 & 1 & x \\ -2 & 2 & -1\end{array}\right)$ is a matrix satisfying AA’ = 9I, find x.

Write the number of vectors of unit length perpendicular to both the vector $\stackrel{\rightarrow}{a}=\stackrel{\wedge}{2i}+\stackrel{\wedge}{j}+\stackrel{\wedge}{2k}$ and ${\vec{b}}={\hat{j}}+{\hat{k}}\,.$

Find ‘λ’ when the projection of $\stackrel{\rightarrow}{a}\$ = $λ\stackrel{\wedge}{i}+\stackrel{\wedge}{j} +4\stackrel{\wedge}{k}$ on $\stackrel{\rightarrow}{b}\$ = $2\stackrel{\wedge}{i}+6\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$ is 4 units.

Give an example of a skew symmetric matrix of order 3.

State the reason why the Relation R = {(a, b) : a ≤ b²} on the set R of real numbers is not reflexive.

Write value of $\textstyle\int$ sec x(sec x + tan x) dx

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