Find the length of the perpendicular drawn from P to `bar(QR)` of the triangle with vertices at P (5,6), Q(-9,1) and R (-3,-1). If A be the mid-point of `bar(QR)`, show that `PQ^(2)+PR^(2)=2(AP^(2)+AQ^(2)).`

find the length of the perpendicular drawn from the point (2,1,-1) on the line x - 2y + 4z = 9

Find the length of the perpendicular drawn from point (2,3,4) to line (4-x)/2=y/6=(1-z)/3dot

The coordinates of the foot of the perpendicular drawn from the point P(1, 2, 1) to the straight line joining the points Q(1, 4, 6) and R(5, 4, 4) are -

Find the coordinates of the foot of the perpendicular drawn from the point P(1,-2) on the line y = 2x +1. Also, find the image of P in the line.

Using integration,find the area of Delta PQR whose vertices are P (2,1) ,Q (3,4) and R( 5,2)

If the points P (a, 1), Q (1, b), R (-2, 11) are collinear and Q be the mid - point of bar(PR) , then find the value of a and b.

PQR is a triangle whose /_Q is right angle. If S is any point on QR, then prove that PS^(2) + QR^(2) =PR^(2) + QS^(2)

If p_(1),p_(2) be the lenghts of perpendiculars from origin on the tangent and the curve x^((2)/(3))+y^((2)/(3))=a^((2)/(3)) drawn at any point on it, show that, 4p_(1)^(2)+p_(2)^(2)=a^(2)

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 the lengths of the perpendiculars from the vertices of a triangle ABC on the opposite sides are p_(1), p_(2), p_(3) then prove that (1)/(p_(1)) + (1)/(p_(2)) + (1)/(p_(3)) = (1)/(r) = (1)/(r_(1)) + (1)/(r_(2)) + (1)/(r_(3)) .