If `vec(alpha) = 2 hat (i) + hat (j) - 3 hat (k) and vec(beta) = hat (i) - 2 hat (j) + hat (k) , ` find a vector of magnitude 5 perpendicular to both `vec (alpha ) and vec (beta)`

Let vec ( a) = hat (i) + 4 hat (j) + 2 hat (k), vec (b) = 3 hat(i) - 2 hat (j) - 7 hat (k) and vec (c ) = 2 hat (i) - hat (j) + 4 hat (k) . Find a vector vec (d) which is perpendicular to both vec (a) and vec (b) and vec ( c) . vec(d) = 18

If vec(a) = 3 hat (i) + 4 hat (j) - hat(k) , vec(b) = hat(i) - 3 hat (j) + 4 hat (k) and vec (c ) = 5 hat (i) - 6 hat (j) + 4 hat (k) , find the vector vec (r ) which is perpendicular to both vec(a) and vec(b) and which satisfies the relation vec(r).vec(c ) = 91

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

If vec(a) = hat(i) + 2 hat(j) - 3 hat (k) and vec(beta) = 3 hat(i) - hat (j) + 2 hat (k) , find the cosine of the angle between the vectors (2 vec(alpha)+ vec(beta)) and (vec(alpha)+2 vec(beta))

Given vec (a) = 4 hat (i) + 5 hat (j) - hat (k), vec(b) = hat (i) - 4 hat (j) + 5 hat (k) If |vec (c ) | = 21 and vec(c ) is perpendicular to vec(a) and vec (b ) , find in component form the vector vec(c )

If vec (a) = 3 hat (i) + 2 hat (j) + 9 hat (k) and vec(b) = hat (i) + lambda hat (j) + 3 hat (k) , then find the value of lambda so that the vectors (vec(a) + vec(b)) and (vec(a) - vec(b)) are perpendicular to each other .

If vec(alpha ) = hat (i) - 2 hat (j) + 3 hat (k) , vec(beta) = 2 hat (i) - 3 hat (j) + hat(k) and vec(gamma) = 3 hat (i) + hat (j) - 2 hat (k) , find vec(alpha) . (vec(beta)xx vec (gamma)) .

If vec(a) = 2 hat (i) - hat (j) + 3 hat (k) and vec(b) = 3 hat (i) + hat (j) - 2 hat (k) , find the angle between the vectors (vec(a) + vec(b)) and (vec(a)-vec(b))

Let vec(a) = hat(i) + hat(j) - 3 hat(k) and vec(b) = 2 hat(i) + hat(j) + hat(k) Statement - I: Vectors vec(a) and vec(b) are perpendicular to each other Statement - II: vec(a) . vec(b) = 0

vec (alpha) = lambda hat (i) + hat (j) + 3 hat (k) , " " vec(beta) = -hat (i) + 2 hat (j) + hat (k) ," " vec(gamma) = 3 hat (i) + hat (j) + 2 hat (k) and [ vec(alpha) vec(beta)vec(gamma)]= -10 then find the value of lambda