If `vec(a)=(2hat(i)+4hat(j)-k^(2)) and vec(b)=(3hat(i)-2hat(j)+lambda hat(k))` be such that `vec(a) _|_ vec(b)` then `lambda=`?

If vec(a)=(2hat(i)+6hat(j)+27hat(k)) and vec(b)=(hat(i)+lambda(j)+mu hat(k)) are such that vec(a)xxvec(b)=vec(0) then find the values of lambda and mu .

(i) If vec(a)=hat(i)+2hat(j)-3hat(k) and vec(b)=3hat(i)-hat(j)+2hat(k) , show that (vec(a)+vec(b)) is perpendicular to (vec(A)-vec(b)) . (ii) If vec(a)=(5hat(i)-hat(j)-3 hat(k)) and vec(b)=(hat(i)+3hat(j)-5hat(k)) then show that (vec(a)+vec(b)) and (vec(a)-vec(b)) are orthogonal.

If vec(a)=(hat(i)-hat(j)+2hat(k)) and vec(b)=(2hat(i)+3hat(j)-4hat(k)) then |vec(a)xx vec(b)|=?

If vec(a)=(hat(i)+2hat(j)-3hat(k)) and vec(b)=(3hat(i)-hat(j)+2hat(k)) then the angle between (vec(a)+vec(b)) and (vec(a)-vec(b)) is

If vec(a)=hat(i)+2hat(j)-3hat(k) and vec(b)=3hat(i)-hat(j)+2hat(k) , then show that (vec(a)+vec(b)) is perpendicular to (vec(a)-vec(b)) .

If vec(a)= 3hat(i) + hat(j) + 2hat(k) and vec(b)= 2hat(i)-2hat(j) + 4hat(k) , then the magnitude of vec(b) xx vec(a) is

Find the value of lambda for which vec(a) and vec(b) are perpendicular, where (i) vec(a)=2hat(i)+lambda hat(j)+hat(k) and vec(b)=(hat(i)-2hat(j)+3hat(k)) (ii) vec(a)=3hat(i)-hat(j)+4hat(k) and vec(b)=- lamnda hat(i)+3 hat(j)+3 hat(k) (iii) vec(A)=2hat(i)+4hat(j)-hat(k) and vec(b)=3 hat(i)-2 hat(j)+lambda hat(k) (iv) vec(a)=3 hat(i)+2 hat(j)-5 hat(k) and vec(b)=-5 hat(j)+lambda hat(k)

If vec(a)=4hat(i)+hat(j)-hat(k) , vec(b)=3hat(i)-2hat(j)+2hat(k) , then the value of |vec(a)-vec(b)-vec(c)| is :-