Vector Lecture 4

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 projection of the vector vecA = hati - 2hatj + hatk on the vector vecB = 4hati - 4hatj + 7hatk is

The x and y components of a vector are 4sqrt3 m and 4 m respectively. What angle does the vector make with positive x-axis ?

Find the unit vector of the vector vec(r ) = 4hat(i) - 2hat(j) + 3 hat(k)

If the magnitude of two vectors are 4 and 6 and the magnitude of their scalar product is 12sqrt2 what is the angle between the vectors?

Consider three vectors veca, vecb and vecc . Vectors veca and vecb are unit vectors having an angle theta between them For vector veca,|veca|^2=veca.veca If veca_|_vecb and veca_|_vecc then veca||vecbxxvecc If veca||vecb, then veca=tvecb Now answer the following question: If |vecc|=4, theta = cos^-1(1/4) and vecc=2vecb+tveca, then t= (A) 3,-4 (B) -3,4 (C) 3,4 (D) -3,-4

Let alpha = (lambda-2) a + b and beta =(4lambda -2)a + 3b be two given vectors where vectors a and b are non-collinear. The value of lambda for which vectors alpha and beta are collinear, 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 a-2b+4c,-2a+3b-6c and -b+2c are coplanar vector, where a,b,c are non-coplanar vectors.

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