Column I, Column II Collinear vectors, p.` vec a` Coinitial vectors, q. ` vec b` Equal vectors, r. ` vec c` Unlike vectors (same intitial point), s. ` vec d`

Show that the vectors vec a - vec b, vec b - vec c , vec c - vec a are coplaner.

If vec a , vec b are two non-collinear vectors, prove that the points with position vectors vec a+ vec b , vec a- vec b and vec a+lambda vec b are collinear for all real values of lambdadot

If vec a , vec b are two non-collinear vectors, prove that the points with position vectors vec a+ vec b , vec a- vec b and vec a+lambda vec b are collinear for all real values of lambdadot

If vec a and vec b are orthogonal unit vectors, then for a vector vec r noncoplanar with vec a and vec b , vec rxx veca is equal to a. [ vec r vec a vec b] vec b-( vec r. vec b)( vec bxx vec a) b. [ vec r vec a vec b]( vec a+ vec b) c. [ vec r vec a vec b] vec a-( vec r. vec a) vec axx vec b d. none of these

Given two vectors vec a=- hat i+2 hat j+2 hat ka n d vec b=-2 hat i+ hat j+2 hat kdot Column I, Column II A vector coplanar with vec aa n d vec b , p. -3 hat i+3 hat j+4 hat k A vector which is perpendicular to both vec aa n d vec b , q. 2 hat i-2 hat j+3 hat k A vector which is equally inclined to vec aa n d vec b , r. hat i+ hat j A vector which forms a triangle with vec aa n d vec b , s. hat i- hat j+5 hat k

If vec c is a unit vector perpendicular to the vectors vec a\ a n d\ vec b write another unit vector perpendicular vec a\ a n d\ vec bdot

If vec a , vec b ,a n d vec c are non-zero vectors such that vec a. vec b= vec a. vec c , then find the geometrical relation between the vectors.

If vec a and vec b are two vectors such that | vec a|=2, |vecb|=3 and ( vec a . vec b )=4 then \ f i n d |( vec a - vec b )|

If P ,Q and R are three collinear points such that vec P Q= vec a and vec Q R = vec bdot Find the vector vec P R .

Volume of parallelepiped formed by vectors vec axx vec b , vec bxx vec ca n d vec cxx vec ai s36s qdot units. Column I|Column II Volume of parallelepiped formed by vectors vec a , vec b ,a n d vec c is|p. 0sq.units Volume of tetrahedron formed by vectors vec a , vec b ,a n d vec c is|q. 12 sq. units Volume of parallelepiped formed by vectors vec a+ vec b , vec b+ vec ca n d vec c+ vec a is|r. 6 sq. units Volume of parallelepiped formed by vectors vec a- vec b , vec b- vec ca n d vec c- vec a is|s. 1 sq. units