Vector Lecture 3

The position vectors of the points P and Q are 5hati+ 7hatj- 2hatk and -3hati+3hatj+6hatk , respectively. Vector vecA= 3hati-hatj+hatk passes through point P and vector vecB=-3hati+2hatj+4hatk passes through point Q. A third vector 2hati+7hatj-5hatk intersects vectors A and B. Find the position vectors of points of intersection.

Seven different lecturers are to deliver lectures in seven perday. A, B and C are three oftne lectures. The number of ways in which a routine for theday canr be made such that A delivers his lecture before B and B before C, is

The vector component of vector vecA =3hati +4hatj +5hatk along vector vecB =hati +hatj +hatk is :

Show that the vectors veca-2vecb+3vecc,-2veca+3vecb-4vecc and - vecb+2vecc are coplanar vector where veca, vecb, vecc are non coplanar vectors

Show that the vectors 2veca-vecb+3vecc, veca+vecb-2vecc and veca+vecb-3vecc are non-coplanar vectors (where veca, vecb, vecc are non-coplanar vectors).

If the magnitudes of two vectors are 3 and 4 and magnitude of their scalar product is 6 what is the angle between the vectors ?

The vector vecB= 5hati+2hatj-Shatk is perpendicular to the vector vecA= 3hati+hatj+2hatk if S =

There are 3 doors to a lecture room. In how many ways can lecturer enter and leave the room ?

There are 3 doors to a lecture room. In how many ways can lecturer enter the room from one door and leave from another door?

A unit vector parallel to vector vecV=(2,-3,6) is vector