सदिश `vec(a) = hat(i) + hat(j) + hat(k)` के परिमाण का परिकलन कीजिए।

Find the projection of vec(a) = 2 hat(i) - hat(j) + hat(k) on vec(b) = hat(i) - 2 hat(j) + hat(k) .

Find the angle between the vectors vec(a) = hat(i) + hat(j) + hat(k) and vec(b) = hat(i) - hat(j) + hat(k) .

If vec (alpha ) = - hat (i) + 2 hat (j) + hat (k) , vec(b) = 3 hat(i) + hat (j) + 2 hat (k) and vec(c ) = 2 hat (i) + hat (j) + 3 hat (k) , find [ vec(c ) vec(a) vec(b)]

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

If vec(A) = hat(i) + hat(j) + hat(k) and B = -hat(i) - hat(j) - hat(k) . Then angle made by (vec(A) - vec(B)) with vec(A) is :

If vec(A) = hat(i) + hat(j) + hat(k) and B = -hat(i) - hat(j) - hat(k) . Then angle made by (vec(A) - vec(B)) with vec(A) is :

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

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) . hat(i)= vec(a).(hat(i)+ hat(j)) = vec(a). ( hat(i) + hat(j) + hat(k)) =1 , then vec(a) is equal to