सदिश `2 hati - 2 hatj + 4 hatk` और `3 hati + hatj`के बीच के कोण की ज्या ( sine ) ज्ञात कीजिए ।

The vectors hati + 2 hatj + 3 hatk, lamda hati+ 4 hatj + 7 hatk,-3 hati - 2 hatj - 5 hatk are collinear if lamda is :

A unit vector coplanar with hati + hatj + 2 hatk and hati + 2 hatj + hatk, and perpendicular to hati + hatj + hatk is : a) ((hatj - hatk )/( sqrt2)) b) ((hati + hatj+ hatk )/( sqrt3)) c) ((hati + hatj + 2 hatk )/( sqrt6)) d) ((hati + 2 hatj + hatk )/( sqrt6))

Find the shortest distance between the lines bar(r) = (4hati - hatj) + lamda(hati + 2hatj - 3hatk) and bar(r) = (hati - hatj + 2hatk) + mu(hati + 4hatj - 5hatk).

If the vectors 2hati-3hatj+4hatk and hati+2hatj-hatk and m hati - hatj+2hatk are coplanar, then the value of m is

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