Compute the magnitude of the following vectors:

Find the values of x and y so that the vectors are equal

For given vectors, and , find the unit vector in the direction of the vector 

Find the direction cosines of the vector 

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are  respectively, in the ration 2:1

(i) internally

(ii) externally

Find the angle between the vectors

Show that each of the given three vectors is a unit vector:

Also, show that they are mutually perpendicular to each other.

Show that is perpendicular to, for any two nonzero vectors

If, then what can be concluded about the vector?

Show that

Given that  and. What can you conclude about the vectors?

If either  or, then. Is the converse true? Justify your answer with an example.

If, then is it true that? Justify your answer.

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors areexternally in the ratio 1: 2. Also, show that P is the mid point of the line segment RQ.