If `p_(1), p _(2), p_(3)` are respectively the perpendicular from the vertices of a triangle to the opposite sides, then find the value of `p_(1) p_(2)p _(3).`

If p(m)=m^(2)-3m+1 , then find the value of p(1) and p(-1) .

If p(t)=t^(3)-1 , find the values of p(1),p(-1),p(0),p(2),p(-2) .

If the points A(6,1), B(8,2), C(9,4) and D(p,3) are the vertices of a parallelogram, taken in order, find the value of p.

If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken inorder, find the value of p.

If p(x)=x^(2)-5x-6 , then find the values of p(1),p(2),p(3),p(0),p(-1),p(-2),p(-3) .

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b , then show that (1)/( p^2) = (1)/( a^2) + (1)/( b^2) .

If (1+3p)/3,(1-p)/1,(1-2p)/2 are the probabilities of 3 mutually exclusive events then find the set of all values of p.

Let A, B, C be the feet of perpendiculars from a point P on the X, Y, Z - axis respectively. Find the coordinates of A, B and C in each of the following where the point P is : (i) P(3, 4, 2) (ii) P(-5, 3, 7) (iii) P(4, -3, -5)

A point P(x,y) nores on the curve x^(2/3) + y^(2/3) = a^(2/3),a >0 for each position (x, y) of p, perpendiculars are drawn from origin upon the tangent and normal at P, the length (absolute valve) of them being p_1(x) and P_2(x) brespectively, then

A planet is made of two materials of density p_(1) and p_(2) as shown in figure. Th acceleration due to gravity at surface of planet is same as a depth 'R'. The ratio of (p_(1))/(p_(2)) is (a)/(b) . Find value of (a^(b)+1)/(86) ( a and b are lowest possible integers)