If overline{PQ} and overline{PR} are two side | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $PQ = a$ and $PR = b$,and let $	heta$ be the angle between them.The area of $\Delta PQR$ is given by $A = \frac{1}{2} ab \sin 	heta$.Let $f(

Vedclass · Accepted Answer

$\pi /2$

Vedclass · Answer

(D) Let $PQ = a$ and $PR = b$,and let $	heta$ be the angle between them.The area of $\Delta PQR$ is given by $A = \frac{1}{2} ab \sin 	heta$.Let $f(	heta) = \frac{1}{2} ab \sin 	heta$.To find the maximum area,we differentiate $f(	heta)$ with respect to $	heta$:$f'(	heta) = \frac{1}{2} ab \cos 	heta$.For maximum area,set $f'(	heta) = 0$:$\frac{1}{2} ab \cos 	heta = 0 \implies \cos 	heta = 0$.Since $0 Using the second derivative test:$f''(	heta) = -\frac{1}{2} ab \sin 	heta$.At $	heta = \frac{\pi}{2}$,$f''(\frac{\pi}{2}) = -\frac{1}{2} ab Since the second derivative is negative,the area is maximum at $	heta = \frac{\pi}{2}$.

If $\overline{PQ}$ and $\overline{PR}$ are two sides of $\Delta PQR$,for what value of the angle between $\overline{PQ}$ and $\overline{PR}$ is the area of the triangle maximum?

Similar Questions

The acceleration $f \text{ ft/sec}^2$ of a particle after a time $t \text{ sec}$ starting from rest is given by $f = 6 - \sqrt{1.2t}$. Then the maximum velocity $v$ and time $T$ to attain this velocity are:

On the interval $[0, 1],$ the function $f(x) = {x^{25}}{(1 - x)^{75}}$ takes its maximum value at the point

If $20$ is divided into two parts such that the product of the cube of one part and the square of the other part is maximum,then these two parts are:

Suppose the cubic $x^3 - px + q$ has three distinct real roots where $p > 0$ and $q > 0$. Then which one of the following holds?

Local maximum and local minimum values of the function $f(x) = (x - 1)(x + 2)^2$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module