Show that `[(vec(a)xxvec(b))xx(vec(a)xxvec(c)))].vec(d)=(veca.vecd)[vecavecbvec(c)]`.

(vec(a) xx vec(b), vec(b) xx vec(a)) =

If vec(a)-vec(i)-2vec(j)-3vec(k), vec(b)=2vec(i)+vec(j)-vec(k) and vec(c )=vec(i)+3vec(j)-2vec(k) , verify that vec(a) xx (vec(b) xx vec(c )) = (vec(a).vec(c ))vec(b)-(vec(a).vec(b))vec(c ) .

If vec(a)= vec(i) + vec(j) + vec(k), vec(b)= 2vec(i)-3vec(j) + vec(k) , then (vec(a) xx vec(b))/(|vec(a) xx vec(b)|) + (vec(b) xx vec(a))/(|vec(b) xx vec(a)|) =

If vec(a) + 2vec(b) + 4vec(c ) = vec(0) then show that vec(a) xx vec(b) =4 (vec(b) xx vec(c ))= 2(vec(c ) xx vec(a))

If vec(a) xx vec(b) = vec(b) xx vec(c )= vec(c )xx vec(a) , where vec(a), vec(b), vec(c ) are non zero vectors, then

Observe the following statements: Assertion (A) : If vertices of a triangle are A(vec(a)), B(vec(b)), C(vec(c )) , then length of altitude through A is (|vec(a) xx vec(b) + vec(b) xx vec(c)+ vec(c ) xx vec(a)|)/(|vec(b)-vec(c )|) Reason (R ): Area of triangle is Delta = (1)/(2) (Base) (Height) = (1)/(2) |vec(AB) xx vec(AC)|