The perimeter P of a rectangle of sides `l\ a n d\ b` is given by `P=2\ (l+b)dot\ ` evaluate the variable and constant part

We know that the perimeter P of a square of side s is given b y\ P=4\ xx\ sdot find the constant and variable part

A B C is an equilateral triangle with A(0,0) and B(a ,0) , (a>0). L, M and N are the foot of the perpendiculars drawn from a point P to the side A B ,B C ,a n dC A , respectively. If P lies inside the triangle and satisfies the condition P L^2=P MdotP N , then find the locus of Pdot

A B C is an equilateral triangle with A(0,0) and B(a ,0) , (a>0). L, M and N are the foot of the perpendiculars drawn from a point P to the side A B ,B C ,a n dC A , respectively. If P lies inside the triangle and satisfies the condition P L^2=P MdotP N , then find the locus of Pdot

In Figure, A B C D is a rectangle. Find the values of x a n d y dot

The position vectors of the vertices of a quadrilateral with A as origin are B( vec b),D( vec d)a n dC(l vec b+m vec d)dot Prove that the area of the quadrialateral is 1/2(l+m)| vec bxx vec d|dot

If P is any arbitrary point on the circumcircle of the equilateral triangle of side length l units, then | vec P A|^2+| vec P B|^2+| vec P C|^2 is always equal to 2l^2 b. 2sqrt(3)l^2 c. l^2 d. 3l^2

If P is any arbitrary point on the circumcirlce of the equllateral trangle of side length l units, then | vec P A|^2+| vec P B|^2+| vec P C|^2 is always equal to 2l^2 b. 2sqrt(3)l^2 c. l^2 d. 3l^2

Let A={a ,\ {b}},f i n d P(A)dot

p\ A N D\ q are any two points lying on the sides D C\ a n d\ A D respectively of a parallelogram A B C Ddot\ Show that a r( A P B)=a r\ ( B Q C)dot

A B is a diameter of a circle C(O ,\ r)dot Chord C D is equal to radius O Cdot If A C\ a n d\ B D when produced intersect at P , prove that /_A P B is constant.