A 10 text{ inches} long pencil AB with midpoi | vedclass

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

Question

(A) Let the pencil be rotated by an angle $\alpha$ about $C$. Let the new position of the pencil be $A'B'$.In the right-angled triangle formed by the

Vedclass · Accepted Answer

$	an^{-1}\left(\frac{3}{4}ight)$

Vedclass · Answer

(A) Let the pencil be rotated by an angle $\alpha$ about $C$. Let the new position of the pencil be $A'B'$.In the right-angled triangle formed by the perpendicular from $P$ to the pencil,let the angle between $PC$ and the new pencil line be $	heta$.We are given $PC = \sqrt{5}$ and the perpendicular distance $d = 1$.In the right triangle formed by $P$,the foot of the perpendicular on the pencil,and $C$,we have $\sin 	heta = \frac{d}{PC} = \frac{1}{\sqrt{5}}$.Thus,$	an 	heta = \frac{1}{2}$.Initially,the angle $\angle PCB = \phi = 	an^{-1}(2)$,so $	an \phi = 2$.The angle of rotation $\alpha$ is the difference between the initial angle $\phi$ and the new angle $	heta$.$\alpha = \phi - 	heta$.$	an \alpha = 	an(\phi - 	heta) = \frac{	an \phi - 	an 	heta}{1 + 	an \phi 	an 	heta} = \frac{2 - 1/2}{1 + 2(1/2)} = \frac{3/2}{2} = \frac{3}{4}$.Therefore,$\alpha = 	an^{-1}\left(\frac{3}{4}ight)$.

Similar Questions

$B(2,3)$,$C(5,-2)$,and $D(1,-1)$ are three points. If $A(x, y)$ is a variable point such that the area of the quadrilateral $ABCD$ is $10 \text{ sq. units}$,then the locus of $A$ is

$A$ line is at a constant distance $c$ from the origin and meets the coordinate axes in $A$ and $B$. The locus of the centre of the circle passing through $O, A, B$ is

$A$ point on the straight line $3x + 5y = 15$ which is equidistant from the coordinate axes will lie in

If the vertices $P$ and $Q$ of a triangle $PQR$ are given by $(2, 5)$ and $(4, -11)$ respectively,and the point $R$ moves along the line $N: 9x + 7y + 4 = 0$,then the locus of the centroid of the triangle $PQR$ is a straight line parallel to

Let $b, d > 0$. The locus of all points $P(r, \theta)$ for which the line $OP$ (where $O$ is the origin) intersects the line $r \sin \theta = b$ at $Q$ such that $PQ = d$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module