Check whether the given three vectors are coplanar or non-coplanar. `-2 hat i-2 hat j+4 hat k ,-2 hat i+4 hat j ,4 hat i-2 hat j-2 hat k`

Prove that the four points having position vectors are non-coplanar: hat i+2hat j+3hat k,2hat i+hat j+3hat k and hat i+hat j+hat k

Prove that the four points having position vectors are coplanar: hat i+hat j+hat k,2hat i+3hat j-hat k and -hat i-2hat j+2hat k

Show that each of the following triads of vectors are coplanar: vec a=hat i-2hat j+3hat k,vec b=-2hat i+3hat j-4hat k,vec c=hat i-3hat j+5hat k

Prove that the four points having position vectors are coplanar: 2hat i-hat j+hat k,hat i-3hat j-5hat k and 3hat i-4hat j-4hat k

Dine the unit vector peroendicular to each of the vectors 3 hat i+ hat j 2 hat k and 2 hat i- 2 hat j = 4 hat k .

Show that each of the following triads of vectors are coplanar: vec a=-4hat i-6hat j-2hat k,vec b=-hat i+4hat j+3hat k,vec c=-8hat i-hat j+3hat k

Show that each of the following triads of vectors are coplanar: vec a= hat i+2 hat j- hat k , vec b=3 hat i+2 hat j+7 hat k , vec c=5 hat i-6 hat j+5 hat k vec a=-4 hat i-6 hat j-2 hat k , vec b=- hat i+4 hat j+3 hat k , vec c=8 hat i- hat j+3 hat k hat a= hat i-2 hat j+3 hat k , vec b=-2 hat i+3 hat j-4 hat k , vec c= hat i-3 hat j+5 hat k

Show that the vectors vec a=-2hat i-2hat j+4hat k,vec b=-2hat i+4hat j-2hat k and vec c=4hat i-2hat j-2hat k are coplanar.

Prove that the following vectors are non- coplanar: 3hat i+hat j-hat k,2hat i-hat j+7hat k and 7hat i-hat j+23hat khat i+2hat j+3hat k,2hat i+hat j+3 and hat i+hat j+hat k

Show that the points whose position vectors are as given below are collinear: 2hat i+hat j-hat k,3hat i-2hat j+hat k and hat i+4hat j-3hat k3hat i-2hat j+4hat k,hat i+hat j+hat k and -hat i+4hat j-2hat k