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if line 2x+7y-1=0 intersect the lines L1:3x+4y+1=0 and L2:6x+8y-3=0 in A and B respectively,then equation of line parallal to L1 and L2 and passes through a point P such that AP:PB=2:1 (internally) is (P is on the line 2x + 7y-1=0)

Find the value of so that the lines l1: (1-x)/3 = (7y-14)/(2lambda) =(z-3)/2 and l2: (7-7x)/(3lambda) = (y-5)/1 = (6-z)/5 are at right angle. Also find the equation of a line passing through the point (3,2,-4) and parallel to l1.

Find the equation of the hyperbola with vertices ( pm 5,0), foci ( pm 7,0)

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Find the equation of the ellipse whose vertices are at (0, pm 4) and foci at (0, pm sqrt7).

If A square matrix such that A^2 = A , then (l+A )^3 -7A is equal to :