l, m and n are three parallel lines intersected by transversals р and q such that l , m and n cut off equal intercepts AB and BC on p (see the given figure). Show that l, m and n cut off equal intercepts DE and EF on q also.

l, m and n are three parallel lines intersected by the transversals p and q at A, B, C and D,E, F such that they make equal intercepts AB and BC on the transversal p. Show that the intercepts DE and EF on q are also equal.

l and m are two parallel lines intersected by another pair of parallel lines p and q . Show that DeltaABC~= DeltaCDA .

If in the given figure, OA=a,OB=b and AP:PB=n:m then OP is equal to

Two parallel lines l and m are intersected by a transversal p (see the given figure). Show that the quadrilateral formed by the bisector of interior angles is a rectangle.

P is a point equidistant from two lines l and m intersecting at point A (see figure). Show that the line AP bisects the angle between them.

If a plane has X-intercept l, Y-intercept m and Z- intercept n, and perpendicular distance of plane from origin is k, then

For positive l, m and n, if the points x=ny+mz, y=lz+nx, z=mx+ly intersect in a straight line, when Q. l, m and n satisfy the equation

Three blocks of masses m, 3m and 5m are connected by massless strings and pulled by a force F on a frictionless surface as shown in the figure below. The tension P in the first string is 16N. If the point of application of F is changed as given below. The values of P' and Q' shall be

Find the angle between the lines whose direction cosines are given by the equation l + m + n = 0 and l^2 + m^2 - n^2 = 0.

A particle of mass m and charge (-q) enters the region between the two charged plates initially moving along x-axis with speed v_x (like particle 1 in figure. The length of plate is L and an uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is qEL^(2)//(2m v_(x)^(2)) . Compare this motion with motion of a projectile in gravitational field discussed in Section 4.10 of Class XI Textbook of Physics.