Find p if the points (p+1,1), (2p + 1,3) and (2p + 2, 2p) are collinear.

Find the condition that the st. lines : p_1x+q_1y=1,p_2x+q_2y=1 and p_3x+q_3y=1 be concurrent, show that the point (p_1,q_1),(p_2,q_2) and (p_3,q_3) are collinear.

Show that the points P(2,6),Q(1,2)and R(3,10) are collinear.

Find the vector joining the points P(2, 3, 0) and Q(– 1, – 2, – 4) directed from P to Q.

In R^3 , consider the planes: P_1: y=0 and P_2:x+z=1 . Let P_3 be a plane, different from P_1 and P_2 , which passes through the intersection of P_1 and P_2 . If the distance of the point (0,1,0) from P_3 is 1 and the distance of a point (alpha, beta, gamma) from P_3 is 2, then which of the following relations is (are) true?

If p_(1),p_(2),p_(3) be the length of perpendiculars from the points (m^(2),2m),(mm',m+m') and (m^('2),2m') respectively on the line xcosalpha+ysinalpha+(sin^(2)alpha)/(cosalpha)=0 then p_(1),p_(2),p_(3) are in:

Perimeter of a triangle is 6p ^(2) - 5p + 10 and two and sides of the triangle are p ^(2) + p -2 and 2p ^(2) - 3p + 5. Find the third side of the triangle.

If overline(P_1P_2) is perpendicular to overline(P_2P_3) , then the value of k is, where P_1(k, 1, -1), P_2(2k, 0, 2) and P_3(2+2k, k, 1) is …..

If P (n) is the statement : "2^(3n)- 1 is an integral multiple of 7”, prove that P(1), P(2) and P (3) are true.