Express the vector `veca=(5hati-2hatj+5hatk)` as sum of two vectors such that one is paralle to the vector `vecb=(3hati+hatk)` and the other is perpendicular to `vecb`.

If the vector vecb = 3hati + 4hatk is written as the sum of a vector vecb_(1) parallel to veca = hati + hatj and a vector vecb_(2) , perpendicular to veca then vecb_(1) xx vecb_(2) is equal to:

Projection of the vector veca=2hati+3hatj-2hatk on the vector vecb=hati+2hatj+3hatk is

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

Find the projection of vector veca=5hati-hatj-3hatk on the vector vecb=hati+hatj+hatk .

The projection of vector veca=2hati+3hatj+2hatk , on the vector vecb=hati+2hatj+hatk is

If veca=hati-2hatj+3hatk, vecb=2hati+3hatj-hatk and vecc=rhati+hatj+(2r-1)hatk are three vectors such that vecc is parallel to the plane of veca and vecb then r is equal to,

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

Find component of vector vec(a)=hati+hatj+3hatk in directions parallel to and perpendicular to vector vecb=hati+hatj .

Find the projection of the vector veca=3hati+2hatj-4hatk on the vector vecb=hati+2hatj+hatk .

If veca =hati + hatj, vecb = hati - hatj + hatk and vecc is a unit vector bot to the vector veca and coplanar with veca and vecb , then a unit vector vecd is perpendicular to both veca and vecc is: