Can you associate vectors with (a) the length of a wire bent into a loop, (b) a plane area, (c) a sphere? Explain.

Using vectors find the area of triangle with vertices A (1,1,2) ,B (2,3,5) and C (1,5,5).

Which vector can be asS0ciated with a plane area? And what is jts direction?

By looking at which internal structure of a plant can you tell whether a plant is C_3 or C_4 ? Explain.

A galvanometer having a resistance of 50Ω gives a full scale deflection for a current of 0.05 A. The length in meter of a resistance wire of area of cross section 3×10^−3 cm^2 that can be used to convert the galvanometer into an ammeter which can read a maximum of 5A current is [specific resistance of the wire =5×10^−7 Ωm]

A square loop of side 3cm is placed 25 cm away from a Convex mirror of focal length 10cm. The aixs of the mirror passes through the intersecting point of the diagonals of the loop and is perpendicular to the plane of the loop. What is the area enclosed by the image of the loop?

If vecu , vecv and vecw be the position vectors of the vertices A,B and C of the DeltaABC find the area of the triangle.

A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination, (a) Will it reach the bottom with the same speed in each case? (b) Will it take longer to roll down one plane than the other? (c) If so, which one and why?

You have studied in Class IX (Chapter 9,Example 3),that a median of a triangle divides in into two triangles of equal areas.Verify this result for triangleABC whose vertices are A(4,-6),B(3,-2) and C(5,2).