In Figure, If the face `E F G H` is taken as the base, then name the lateral faces. Also, name the line segment representing the height of the cuboid.

In a parallelogram OABC, vectors vec a, vec b, vec c are respectively the positions of vectors of vertices A, B, C with reference to O as origin. A point E is taken on the side BC which divide the line 2:1 internally. Also the line segment AE intersect the line bisecting the angle O internally in point P. If CP, when extended meets AB in point F. Then The position vector of point P, is

Is it true that a cuboid is also known as a rectangular prism? What is the shape of the lateral faces of this prism?

For the cuboid show in Figure. What is the base of this cuboid? What are the lateral faces of this cuboid? Name one pair of opposite faces. How many pairs of opposite faces are there? Name them. Name all the faces of this cuboid which have X as a vertex.

A liquid of density rho is filled in a beaker of cross section S to a height H and then a cylinder of mass m and corss section s is made to float in it as shown in figure. It the atmospheric pressure is p_(0) , find the pressure a at the top face A of the cylinder b at the botom face C of the cylinder and c. at the base B of the beaker. Can ever these three pressures be equal?

A wooden bookshelf has external dimensions as follows: H e igh t=110c m ,D e p t h=25 c m ,B r e a dt h=85 c m (See Figure). The thickness of the plank is 5c m everywhere. The external faces are to be polished and the inner face are to be painted. If the rate of polishing is 20 p a i s e p e r c m^2 and if the rate of painting is 10 paise per cm^2 . Find total cost of expenses.

V =1/3 pi ((d)/(2)) ^(2) h A circle of rubber with a constant diameter d is placed on a table, its perimeter is anchored to the table and a string is attached to its centre. When the string is pulled upwards, a cone is formed with height h and volume V. The relationship between d, h, and V is represented above. Which of the following statements must be true ? I. As the volume of the cone decreases, the height also decreases. II. If the diameter of the base of the cone is 6 centimeters, the height can be determined by dividing the volume by 3pi. III. If the height of the conc triples, the volume must also triple.

An isosceles triangle of wood of base 2a and height h is placed with its base on the ground vertex directly above. The triangle faces the sun whose altitude is 30^@ . Then, the tangent of the angle at the apex of the shadow is

The electric field vecE_1 at one face of a parallelopiped is uniform over the entire face and is directed out of the face. At the opposite face, the electric field vecE_2 is also uniform over the entire face and is directed into that face (as shown in figure). The two faces in question are inclined at 30^@ from the horizontal, vecE_1 and vecE_2 (both horizontal) have magnitudes of 2.50 xx 10^(4) NC^(-1) and 7.00 xx 10^(4)NC^(-1) . respectively. Assuming that no other electric field lines cross the surfacesof the parallelopiped, the net charge contained with in is

Name the blank spaces a, b, c, d, e, f and g given in the following table: