If `vec(a)=`

If |vec(a)|= |vec(b)| =1 and |vec(a) xx vec(b)|= vec(a).vec(b) , then |vec(a) + vec(b)|^(2)=

If vec(u)= vec(a)- vec(b), vec(v)= vec(a) + vec(b) and |vec(a)| =|vec(b)|=2 , then |vec(u) xx vec(v)| =

If vec(p)= vec(a)-vec(b), vec(q)= vec(a) + vec(b), |vec(a)|= |vec(b)|=t " then " |vec(p) xx vec(q)| =

Let vec(a), vec(b), vec(c) be non-coplanar vectors and vec(p)=(vec(b)xxvec(c))/([vec(a)vec(b)vec(c)]), vec(q)=(vec(c)xxvec(a))/([vec(a)vec(b)vec(c)]), vec(r)=(vec(a)xxvec(b))/([vec(a)vec(b)vec(c)]) . What is the value of (vec(a)-vec(b)-vec(c)).vec(p)+(vec(b)-vec(c)-vec(a)).vec(q)+(vec(c)-vec(a)-vec(b)).vec(r) ?

[vec(a)vec(b)vec(c )]=[vec(b)vec(c )vec(a)]=[vec(c )vec(a)vec(b)] .

vec(a)+vec(b)+vec(c)=vec(0) such that |vec(a)|=3, |vec(b)|=5 and |vec(c)|=7 . What is vec (a). vec(b) + vec(b). vec(c) + vec(c). vec (a) equal to ?

If |vec a| = 3, |vec b| = 5, and |vec c| = 4 and vec a + vec b + vec c = vec O then the value of (vec a . vec b + vec b . vec c + vec c .vec a ) =

Assertion: If |vec(A)+vec(B)|=|vec(A)-vec(B)| , then angle between vec(A) and vec(B) is 90^(@) Reason: vec(A)+vec(B)= vec(B)+vec(A)

Prove that |vec(a)xx vec(b)|^(2)=|vec(a)|^(2)|vec(b)|^(2)-(vec(a).vec(b))^(2) =|(vec(a).vec(a),vec(a).vec(b)),(vec(a).vec(b),vec(b).vec(b))| .