A vector has magnitude and direction (i) Does it have a location in the space ? (ii) Can it vary with time ? (iii) Will two equal vectors ` vec a` and `vec b` different locations in space necessarily have identical physical effects ? Give examples in support of your answer.

Find the angle between two vectors vec a and vec b with magnitudes sqrt3 and 2, respectivey having vec a. vec b = sqrt6 .

Answer the following as true or false. (i) A zero vector cannot be assigned a definite direction. (ii) A zero vector may be regarded as having any direction. (iii) Two vectors are equal if they have same magnitude and direction regardless of the position of their initial points. (iv) The length of a unit vector is 2.

Two vectors of equal magnitude of 5 unit have an angle 60^0 between them. Find the magnitude of (a) the sum of the vectors and (b) the difference of the vectors. . .

Two vectors in space are equal only if they have equal component in a. a given direction b. two given directions c. three given directions d. in any arbitrary direction

Find the magnitude of two vectors veca and vec b having the same magnitude such that the angle between them is 30^(@) and their scalar product is sqrt3 .

Find the magnitude of two vectors vec a and vec b having the same magnitude and such that the angle between them is 60^(@) and their scalar products is 1/2.

If vec(A) = 3 hat(i) + 4 hat(j) and vec(B) = 7 hat(i) + 24 hat(j) , then find a vector having the same magnitudes as vec(B) and parallel to vec(A) .

Vectors vec a=-4 hat i+3 hat k ; vec b=14 hat i+2 hat j-5 hat k are laid off from one point. Vector hat d , which is being laid of from the same point dividing the angle between vectors vec aa n d vec b in equal halves and having the magnitude sqrt(6), is a. hat i+ hat j+2 hat k b. hat i- hat j+2 hat k c. hat i+ hat j-2 hat k d. 2 hat i- hat j-2 hat k

Answer the following questions . a. The earth's magnetic field varies from point is space. Does it also change with time ? It so , on what time scate does it change appreciably ? b. The earth's core is known to contain iron. Yet geologists do not regard this as a source of the earth's magnetism why ? c. The charged currents in the outer conducting regions of the earth's core are thought to be responsible for earth's magnetism . What might be the ' battery ' (i.e., the source of energy) to sustain these currents ? d. The earth may have even reversed the direction of its field several times during its history of 4 to 5 billion years. How can geologists know about the earth's field in such distant past ? e. The earth's field departs from its dipole substantially at large distances (greater than about 30,000 km) what agencies may be responsible for this distortion ? f. Interstellar space has an extremely weak magnetic field of the order of 10^(-12) T, Can such a weak field be of any significant consequence ? Explain. [Note : Exercise 2 is meant mainly to arouse your curiosity . Answers to some question above are tentative or unknown . Brief answers wherever possible are given at the end . For details , you should consult a good text on geomagnetism.]