Question

For what value of λ are the vectors $\stackrel{\wedge}{i}+2λ \stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $2\stackrel{\wedge}{i}+\stackrel{\wedge}{j} -3\stackrel{\wedge}{k}$ perpendicular ?

Find the projection of vector $\stackrel{\rightarrow}{a}\$ = $2\stackrel{\wedge}{i}+3\stackrel{\wedge}{j} +2\stackrel{\wedge}{k}$ on the vector $\stackrel{\rightarrow}{b}\$ = $2\stackrel{\wedge}{i}+2\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$

Write the degree of the differential equation : $\left({\frac{d^{2}y}{d x^{2}}}\right)^{2}-2{\frac{d^{2}y}{d x^{2}}}-{\frac{d y}{d x}}+1=0.$

What is the degree of the following differential equation ? $5x\biggl(\frac{d y}{d x}\biggr)^{2}-\frac{d^{2}y}{d x^{2}}-6y\;=\log x.$

If A = {1, 2, 3}, B = {4, 5, 6, 7} and f = {(1, 4), (2, 5),(3, 6)} is a function from A to B. State whether f is one-one or not.

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 ${\vec{AB}}+{\vec{BC}}+{\vec{C A}}$ ?