Question

Find the area of the parallelogram whose diagonals are represented by the vectors $\stackrel{\rightarrow}{a}\$ = $2{\hat{i}}-3{\hat{j}}+4{\hat{k}}$ and ${\vec{b}}=2{\hat{i}}-{\hat{j}}+2{\hat{k}}$

If E and F be two events such that P(E) = 1/3, P(F) = 1/4, find P(E U F) if E and F are independent events.

Find : $\textstyle\int$$\textstyle\left\{{\frac{\left(x+\sin^{2}x\right)\sec^{2}x}{1+x^{2}}}\right\}d x~.$

Find the general solution of the differential equation ${\frac{d y}{d x}}+{\frac{2}{x}}y=x$

Find the particular solution of the differential equation ${\frac{d y}{d x}}={\frac{1+y^{2}}{1+x^{2}}}$ given that y(0) = ${\sqrt{3}}.$

Find : $\textstyle\int$${\sqrt{x^{2}-2x}}\ d x$

The volume of a sphere is increasing at the rate of 8 cm³/sec. Find the rate at which its surface area is increasing when the radius of the sphere is 12 cm.