Question

Write the value of λ so that the vectors $\stackrel{\rightarrow}{a}\$ = $2 \stackrel{\wedge}{i}+λ\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $\stackrel{\rightarrow}{b}\$ = $\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$ are perpendicular to each other ?

If $\left(\begin{array}{l l }2x+y & 3y \\ 0 & 4\end{array}\right)$ = $\left(\begin{array}{l l }6 & 0 \\ 0 & 4\end{array}\right)$ then find the value of x.

Find x from the matrix equation $\left(\begin{array}{l l }1 & 3 \\ 4 & 5\end{array}\right)$ $\left(\begin{array}{l }x \\ 2\end{array}\right)$ = $\left(\begin{array}{l }5 \\ 6\end{array}\right)$ .

Evaluate : $\textstyle\int\!{\frac{\ d x}{\sin^{2}x\cos^{2}x}}$ .

Write the value of $\stackrel{\rightarrow}{p}\$ for which the vectors $3\stackrel{\wedge}{i}+2\stackrel{\wedge}{j} +9\stackrel{\wedge}{k}$ and $\stackrel{\wedge}{i}-2p\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$ are parallel vectors.

Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} given by f = {(1, 2) (3, 5) (4, 1)} and g = {(1, 3), (2, 3), (5, 1)} Write down gof.

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