If `vec(OA)=2hati-hatj+hatk, vec(OB)=hati-3hatj-5hatk and vec(OC)=3hati-3hatj-3hatk` then show that CB is perpendicular to AC.

Let vec a=4hati+5hatj-hatk, vecb = hati -4hatj+5hatk and vec c=3hati+hatj-hatk . Find a vector vec d which is perpendicular to both vec c and vec b and vec d.vec a=21

If veca=2hati+3hatj+hatk, vecb=hati-2hatj+hatk and vecc=-3hati+hatj+2hatk , then [veca vecb vecc]=

If veca=2hati+3hatj+hatk, vecb=hati-2hatj+hatk and vecc=-3hati+hatj+2hatk , then [veca vecb vecc]=

If a=3hati-2hatj+hatk,b=2hati-4hatj-3hatk and c=-hati+2hatj+2hatk , then a+b+c is

If vec r = 3 hati + 2 hatj - 5 hatk , vec a= 2 hati - hatj + hatk, vec b = hati + 3 hatj - 2hatk and vec c=-2 hati + hatj - 3 hatk " such that " hat r = x vec a +y vec b + z vec c then

Given veca=1/7 (2hati+3hatj+6hatk), vec= 1/7 (3hati-6hatj+2hatk) and vecc1/7(6hati+2hatj-3hatk) . Show that veca,vecb,vecc are of unit length mutually perpendicular and that vecaxxvecb=vecc .

The lines vecr=(2hati-3hatj+7hatk)+lamda(2hati+phatj+5hatk) and vecr=(hati+2hatj+3hatk)+mu(3hati+phatj+phatk) are perpendicular it p=

Let veca=hati+2hatj +hatk, vec=hati-hatj+hatk and vecc=hati+hatj-hatk . A vector in the plane of veca and vecb whose projection on vecc is 1/sqrt(3) is (A) 4hati-hatj+4hatk (B) hati+hatj-3hatk (C) 2hati+hatj-2hatk (D) 4hati+hatj-4hatk

If veca=5hati-hatj-3hatk and vecb=hati+3hatj-5hatk , then show that the vectors veca+vecb and veca-vecb are perpendicular.

If vecF=3hati-4hatj+5hatk " and " vecS=6hati+2hatj+5hatk , the find the work done.