Question

Find the sum of the vectors $\stackrel{\rightarrow}{a}=\hat{i}-2\hat{j}+\hat{k}\;,$ $\vec{b}=-2\hat{i}+4\hat{j}+5\hat{k}$ and $\stackrel{\rightarrow}{c}=\hat{i}-6\hat{j}-7\hat{k}.$

If the following function f(x) is continuous at x = 0, then write the value of k.

Write the value of : $\textstyle\int{\frac{x+\cos6.x}{3\,x^{2}\,+\,\sin6.x}}\,d x\,.$

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

Simplify : cosθ $\left(\begin{array}{l l }cosθ & sinθ \\ -sinθ & cosθ\end{array}\right)$ + sinθ $\left(\begin{array}{l l }sinθ & -cosθ \\ cosθ & sinθ\end{array}\right)$

For a 2 x 2 matrix, A = [$a_{i j}$] whose elements are given by $a_{i j}$ = $i/j,$ write the value of $a_{12}\,.$

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.